Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(−56+210,−4+210)(x2,y2)=(−56+42,−4+42)(x3,y3)=(5−6+42,−4−42)(x4,y4)=(56+210,−4+210)(x5,y5)=(56+42,−4+42)(x6,y6)=(56−42,−4−42)
Evaluate
{x5×3∣y−2∣=12x5−y=10
Calculate
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Evaluate
x5×3∣y−2∣
Multiply the terms
3x5∣y−2∣
Multiply the terms
3x5(y−2)
{3x5(y−2)=12x5−y=10
Solve the equation for y
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Evaluate
x5−y=10
Move the expression to the right-hand side and change its sign
−y=10−x5
Change the signs on both sides of the equation
y=−10+x5
{3x5(y−2)=12y=−10+x5
Substitute the given value of y into the equation 3x5(y−2)=12
3x5(−10+x5−2)=12
Simplify
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Evaluate
3x5(−10+x5−2)
Subtract the numbers
3x5(−12+x5)
Multiply the terms
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Evaluate
x5(−12+x5)
Use the the distributive property to expand the expression
x5(−12)+x5x5
Use the commutative property to reorder the terms
−12x5+x5x5
3−12x5+x5x5
Calculate the absolute value
312x5−x5x5
312x5−x5x5=12
Divide both sides
3312x5−x5x5=312
Divide the numbers
12x5−x5x5=312
Divide the numbers
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Evaluate
312
Reduce the numbers
14
Calculate
4
12x5−x5x5=4
Separate the equation into 2 possible cases
12x5−x5x5=4∪12x5−x5x5=−4
Solve the equation for x
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Evaluate
12x5−x5x5=4
Move the expression to the left side
12x5−x5x5−4=0
Separate the equation into 2 possible cases
12x5−x5×x5−4=0,x5≥012x5−x5(−x5)−4=0,x5<0
Solve the equation
More Steps
Evaluate
12x5−x5×x5−4=0
Calculate
12x5−x10−4=0
Solve the equation using substitution t=x5
12t−t2−4=0
Rewrite in standard form
−t2+12t−4=0
Multiply both sides
t2−12t+4=0
Substitute a=1,b=−12 and c=4 into the quadratic formula t=2a−b±b2−4ac
t=212±(−12)2−4×4
Simplify the expression
t=212±128
Simplify the radical expression
t=212±82
Separate the equation into 2 possible cases
t=212+82t=212−82
Simplify the expression
t=6+42t=212−82
Simplify the expression
t=6+42t=6−42
Evaluate the logic
t=6+42∪t=6−42
Substitute back
x5=6+42∪x5=6−42
Solve the equation for x
x=56+42∪x5=6−42
Solve the equation for x
x=56+42∪x=56−42
x=56+42∪x=56−42,x5≥012x5−x5(−x5)−4=0,x5<0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
x=56+42∪x=56−42,x≥012x5−x5(−x5)−4=0,x5<0
Solve the equation
More Steps
Evaluate
12x5−x5(−x5)−4=0
Calculate
12x5+x5×x5−4=0
Calculate
12x5+x10−4=0
Solve the equation using substitution t=x5
12t+t2−4=0
Rewrite in standard form
t2+12t−4=0
Substitute a=1,b=12 and c=−4 into the quadratic formula t=2a−b±b2−4ac
t=2−12±122−4(−4)
Simplify the expression
t=2−12±160
Simplify the radical expression
t=2−12±410
Separate the equation into 2 possible cases
t=2−12+410t=2−12−410
Simplify the expression
t=−6+210t=2−12−410
Simplify the expression
t=−6+210t=−6−210
Evaluate the logic
t=−6+210∪t=−6−210
Substitute back
x5=−6+210∪x5=−6−210
Solve the equation for x
x=5−6+210∪x5=−6−210
Solve the equation for x
x=5−6+210∪x=−56+210
x=56+42∪x=56−42,x≥0x=5−6+210∪x=−56+210,x5<0
The only way a base raised to an odd power can be less than 0 is if the base is less than 0
x=56+42∪x=56−42,x≥0x=5−6+210∪x=−56+210,x<0
Find the intersection
x=56+42∪x=56−42x=5−6+210∪x=−56+210,x<0
Find the intersection
x=56+42∪x=56−42x=−56+210
Find the union
x=56+42∪x=56−42∪x=−56+210
x=56+42∪x=56−42∪x=−56+210∪12x5−x5x5=−4
Solve the equation for x
More Steps
Evaluate
12x5−x5x5=−4
Move the expression to the left side
12x5−x5x5−(−4)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
12x5−x5x5+4=0
Separate the equation into 2 possible cases
12x5−x5×x5+4=0,x5≥012x5−x5(−x5)+4=0,x5<0
Solve the equation
More Steps
Evaluate
12x5−x5×x5+4=0
Calculate
12x5−x10+4=0
Solve the equation using substitution t=x5
12t−t2+4=0
Rewrite in standard form
−t2+12t+4=0
Multiply both sides
t2−12t−4=0
Substitute a=1,b=−12 and c=−4 into the quadratic formula t=2a−b±b2−4ac
t=212±(−12)2−4(−4)
Simplify the expression
t=212±160
Simplify the radical expression
t=212±410
Separate the equation into 2 possible cases
t=212+410t=212−410
Simplify the expression
t=6+210t=212−410
Simplify the expression
t=6+210t=6−210
Evaluate the logic
t=6+210∪t=6−210
Substitute back
x5=6+210∪x5=6−210
Solve the equation for x
x=56+210∪x5=6−210
Solve the equation for x
x=56+210∪x=56−210
x=56+210∪x=56−210,x5≥012x5−x5(−x5)+4=0,x5<0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
x=56+210∪x=56−210,x≥012x5−x5(−x5)+4=0,x5<0
Solve the equation
More Steps
Evaluate
12x5−x5(−x5)+4=0
Calculate
12x5+x5×x5+4=0
Calculate
12x5+x10+4=0
Solve the equation using substitution t=x5
12t+t2+4=0
Rewrite in standard form
t2+12t+4=0
Substitute a=1,b=12 and c=4 into the quadratic formula t=2a−b±b2−4ac
t=2−12±122−4×4
Simplify the expression
t=2−12±128
Simplify the radical expression
t=2−12±82
Separate the equation into 2 possible cases
t=2−12+82t=2−12−82
Simplify the expression
t=−6+42t=2−12−82
Simplify the expression
t=−6+42t=−6−42
Evaluate the logic
t=−6+42∪t=−6−42
Substitute back
x5=−6+42∪x5=−6−42
Solve the equation for x
x=5−6+42∪x5=−6−42
Solve the equation for x
x=5−6+42∪x=−56+42
x=56+210∪x=56−210,x≥0x=5−6+42∪x=−56+42,x5<0
The only way a base raised to an odd power can be less than 0 is if the base is less than 0
x=56+210∪x=56−210,x≥0x=5−6+42∪x=−56+42,x<0
Find the intersection
x=56+210x=5−6+42∪x=−56+42,x<0
Find the intersection
x=56+210x=5−6+42∪x=−56+42
Find the union
x=56+210∪x=5−6+42∪x=−56+42
x=56+42∪x=56−42∪x=−56+210∪x=56+210∪x=5−6+42∪x=−56+42
Rearrange the terms
{x=56+42y=−10+x5∪{x=56−42y=−10+x5∪{x=−56+210y=−10+x5∪{x=56+210y=−10+x5∪{x=5−6+42y=−10+x5∪{x=−56+42y=−10+x5
Calculate
More Steps
Evaluate
{x=56+42y=−10+x5
Substitute the given value of x into the equation y=−10+x5
y=−10+(56+42)5
Simplify the expression
More Steps
Evaluate
−10+x5
Substitute back
−10+(56+42)5
Calculate the absolute value
−10+6+42
Add the numbers
−4+42
y=−4+42
Calculate
{x=56+42y=−4+42
{x=56+42y=−4+42∪{x=56−42y=−10+x5∪{x=−56+210y=−10+x5∪{x=56+210y=−10+x5∪{x=5−6+42y=−10+x5∪{x=−56+42y=−10+x5
Calculate
More Steps
Evaluate
{x=56−42y=−10+x5
Substitute the given value of x into the equation y=−10+x5
y=−10+(56−42)5
Simplify the expression
More Steps
Evaluate
−10+x5
Substitute back
−10+(56−42)5
Calculate the absolute value
−10+6−42
Add the numbers
−4−42
y=−4−42
Calculate
{x=56−42y=−4−42
{x=56+42y=−4+42∪{x=56−42y=−4−42∪{x=−56+210y=−10+x5∪{x=56+210y=−10+x5∪{x=5−6+42y=−10+x5∪{x=−56+42y=−10+x5
Calculate
More Steps
Evaluate
{x=−56+210y=−10+x5
Substitute the given value of x into the equation y=−10+x5
y=−10+(−56+210)5
Simplify the expression
More Steps
Evaluate
−10+x5
Substitute back
−10+(−56+210)5
Calculate the absolute value
−10+6+210
Add the numbers
−4+210
y=−4+210
Calculate
{x=−56+210y=−4+210
{x=56+42y=−4+42∪{x=56−42y=−4−42∪{x=−56+210y=−4+210∪{x=56+210y=−10+x5∪{x=5−6+42y=−10+x5∪{x=−56+42y=−10+x5
Calculate
More Steps
Evaluate
{x=56+210y=−10+x5
Substitute the given value of x into the equation y=−10+x5
y=−10+(56+210)5
Simplify the expression
More Steps
Evaluate
−10+x5
Substitute back
−10+(56+210)5
Calculate the absolute value
−10+6+210
Add the numbers
−4+210
y=−4+210
Calculate
{x=56+210y=−4+210
{x=56+42y=−4+42∪{x=56−42y=−4−42∪{x=−56+210y=−4+210∪{x=56+210y=−4+210∪{x=5−6+42y=−10+x5∪{x=−56+42y=−10+x5
Calculate
More Steps
Evaluate
{x=5−6+42y=−10+x5
Substitute the given value of x into the equation y=−10+x5
y=−10+(5−6+42)5
Simplify the expression
More Steps
Evaluate
−10+x5
Substitute back
−10+(5−6+42)5
Calculate the absolute value
−10+6−42
Add the numbers
−4−42
y=−4−42
Calculate
{x=5−6+42y=−4−42
{x=56+42y=−4+42∪{x=56−42y=−4−42∪{x=−56+210y=−4+210∪{x=56+210y=−4+210∪{x=5−6+42y=−4−42∪{x=−56+42y=−10+x5
Calculate
More Steps
Evaluate
{x=−56+42y=−10+x5
Substitute the given value of x into the equation y=−10+x5
y=−10+(−56+42)5
Simplify the expression
More Steps
Evaluate
−10+x5
Substitute back
−10+(−56+42)5
Calculate the absolute value
−10+6+42
Add the numbers
−4+42
y=−4+42
Calculate
{x=−56+42y=−4+42
{x=56+42y=−4+42∪{x=56−42y=−4−42∪{x=−56+210y=−4+210∪{x=56+210y=−4+210∪{x=5−6+42y=−4−42∪{x=−56+42y=−4+42
Calculate
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Check the solution
More Steps
Check the solution
⎩⎨⎧(−56+210)5×3−4+210−2=12(−56+210)5−(−4+210)=10
Simplify
{12=1210=10
Evaluate
true
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Check the solution
More Steps
Check the solution
⎩⎨⎧(−56+42)5×3−4+42−2=12(−56+42)5−(−4+42)=10
Simplify
{12=1210=10
Evaluate
true
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Check the solution
More Steps
Check the solution
⎩⎨⎧(56−42)5×3−4−42−2=12(56−42)5−(−4−42)=10
Simplify
{12=1210=10
Evaluate
true
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Check the solution
More Steps
Check the solution
⎩⎨⎧(56+210)5×3−4+210−2=12(56+210)5−(−4+210)=10
Simplify
{12=1210=10
Evaluate
true
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Check the solution
More Steps
Check the solution
⎩⎨⎧(56+42)5×3−4+42−2=12(56+42)5−(−4+42)=10
Simplify
{12=1210=10
Evaluate
true
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Check the solution
More Steps
Check the solution
⎩⎨⎧(56−42)5×3−4−42−2=12(56−42)5−(−4−42)=10
Simplify
{12=1210=10
Evaluate
true
{x=−56+210y=−4+210∪{x=−56+42y=−4+42∪{x=5−6+42y=−4−42∪{x=56+210y=−4+210∪{x=56+42y=−4+42∪{x=56−42y=−4−42
Solution
(x1,y1)=(−56+210,−4+210)(x2,y2)=(−56+42,−4+42)(x3,y3)=(5−6+42,−4−42)(x4,y4)=(56+210,−4+210)(x5,y5)=(56+42,−4+42)(x6,y6)=(56−42,−4−42)
Show Solution
