Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(811+333,2−11+333)(x2,y2)=(811−333,−211+333)
Evaluate
{xy=4x−y4x−y=11
Solve the equation for y
More Steps
Evaluate
4x−y=11
Move the expression to the right-hand side and change its sign
−y=11−4x
Change the signs on both sides of the equation
y=−11+4x
{xy=4x−yy=−11+4x
Substitute the given value of y into the equation xy=4x−y
x(−11+4x)=4x−(−11+4x)
Simplify
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Evaluate
4x−(−11+4x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4x+11−4x
The sum of two opposites equals 0
More Steps
Evaluate
4x−4x
Collect like terms
(4−4)x
Add the coefficients
0×x
Calculate
0
0+11
Remove 0
11
x(−11+4x)=11
Expand the expression
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Evaluate
x(−11+4x)
Apply the distributive property
x(−11)+x×4x
Use the commutative property to reorder the terms
−11x+x×4x
Multiply the terms
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Evaluate
x×4x
Use the commutative property to reorder the terms
4x×x
Multiply the terms
4x2
−11x+4x2
−11x+4x2=11
Move the expression to the left side
−11x+4x2−11=0
Rewrite in standard form
4x2−11x−11=0
Substitute a=4,b=−11 and c=−11 into the quadratic formula x=2a−b±b2−4ac
x=2×411±(−11)2−4×4(−11)
Simplify the expression
x=811±(−11)2−4×4(−11)
Simplify the expression
More Steps
Evaluate
(−11)2−4×4(−11)
Multiply
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Multiply the terms
4×4(−11)
Rewrite the expression
−4×4×11
Multiply the terms
−176
(−11)2−(−176)
Rewrite the expression
112−(−176)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
112+176
Evaluate the power
121+176
Add the numbers
297
x=811±297
Simplify the radical expression
More Steps
Evaluate
297
Write the expression as a product where the root of one of the factors can be evaluated
9×33
Write the number in exponential form with the base of 3
32×33
The root of a product is equal to the product of the roots of each factor
32×33
Reduce the index of the radical and exponent with 2
333
x=811±333
Separate the equation into 2 possible cases
x=811+333x=811−333
Evaluate the logic
x=811+333∪x=811−333
Rearrange the terms
{x=811+333y=−11+4x∪{x=811−333y=−11+4x
Calculate
More Steps
Evaluate
{x=811+333y=−11+4x
Substitute the given value of x into the equation y=−11+4x
y=−11+4×811+333
Calculate
y=2−11+333
Calculate
{x=811+333y=2−11+333
{x=811+333y=2−11+333∪{x=811−333y=−11+4x
Calculate
More Steps
Evaluate
{x=811−333y=−11+4x
Substitute the given value of x into the equation y=−11+4x
y=−11+4×811−333
Calculate
y=−211+333
Calculate
{x=811−333y=−211+333
{x=811+333y=2−11+333∪{x=811−333y=−211+333
Check the solution
More Steps
Check the solution
{811+333×2−11+333=4×811+333−2−11+3334×811+333−2−11+333=11
Simplify
{11=1111=11
Evaluate
true
{x=811+333y=2−11+333∪{x=811−333y=−211+333
Check the solution
More Steps
Check the solution
⎩⎨⎧811−333×(−211+333)=4×811−333−(−211+333)4×811−333−(−211+333)=11
Simplify
{11=1111=11
Evaluate
true
{x=811+333y=2−11+333∪{x=811−333y=−211+333
Solution
(x1,y1)=(811+333,2−11+333)(x2,y2)=(811−333,−211+333)
Show Solution
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