Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(107+321,2−7+321)(x2,y2)=(107−321,−27+321)
Evaluate
{xy=5x−y5x−y=7
Solve the equation for y
More Steps
Evaluate
5x−y=7
Move the expression to the right-hand side and change its sign
−y=7−5x
Change the signs on both sides of the equation
y=−7+5x
{xy=5x−yy=−7+5x
Substitute the given value of y into the equation xy=5x−y
x(−7+5x)=5x−(−7+5x)
Simplify
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Evaluate
5x−(−7+5x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5x+7−5x
The sum of two opposites equals 0
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Evaluate
5x−5x
Collect like terms
(5−5)x
Add the coefficients
0×x
Calculate
0
0+7
Remove 0
7
x(−7+5x)=7
Expand the expression
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Evaluate
x(−7+5x)
Apply the distributive property
x(−7)+x×5x
Use the commutative property to reorder the terms
−7x+x×5x
Multiply the terms
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Evaluate
x×5x
Use the commutative property to reorder the terms
5x×x
Multiply the terms
5x2
−7x+5x2
−7x+5x2=7
Move the expression to the left side
−7x+5x2−7=0
Rewrite in standard form
5x2−7x−7=0
Substitute a=5,b=−7 and c=−7 into the quadratic formula x=2a−b±b2−4ac
x=2×57±(−7)2−4×5(−7)
Simplify the expression
x=107±(−7)2−4×5(−7)
Simplify the expression
More Steps
Evaluate
(−7)2−4×5(−7)
Multiply
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Multiply the terms
4×5(−7)
Rewrite the expression
−4×5×7
Multiply the terms
−140
(−7)2−(−140)
Rewrite the expression
72−(−140)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
72+140
Evaluate the power
49+140
Add the numbers
189
x=107±189
Simplify the radical expression
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Evaluate
189
Write the expression as a product where the root of one of the factors can be evaluated
9×21
Write the number in exponential form with the base of 3
32×21
The root of a product is equal to the product of the roots of each factor
32×21
Reduce the index of the radical and exponent with 2
321
x=107±321
Separate the equation into 2 possible cases
x=107+321x=107−321
Evaluate the logic
x=107+321∪x=107−321
Rearrange the terms
{x=107+321y=−7+5x∪{x=107−321y=−7+5x
Calculate
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Evaluate
{x=107+321y=−7+5x
Substitute the given value of x into the equation y=−7+5x
y=−7+5×107+321
Calculate
y=2−7+321
Calculate
{x=107+321y=2−7+321
{x=107+321y=2−7+321∪{x=107−321y=−7+5x
Calculate
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Evaluate
{x=107−321y=−7+5x
Substitute the given value of x into the equation y=−7+5x
y=−7+5×107−321
Calculate
y=−27+321
Calculate
{x=107−321y=−27+321
{x=107+321y=2−7+321∪{x=107−321y=−27+321
Check the solution
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Check the solution
{107+321×2−7+321=5×107+321−2−7+3215×107+321−2−7+321=7
Simplify
{7=77=7
Evaluate
true
{x=107+321y=2−7+321∪{x=107−321y=−27+321
Check the solution
More Steps
Check the solution
⎩⎨⎧107−321×(−27+321)=5×107−321−(−27+321)5×107−321−(−27+321)=7
Simplify
{7=77=7
Evaluate
true
{x=107+321y=2−7+321∪{x=107−321y=−27+321
Solution
(x1,y1)=(107+321,2−7+321)(x2,y2)=(107−321,−27+321)
Show Solution
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