Algebra
Calculus
Trigonometry
Matrix
Question
{xy=72x−y=5
Solve the system of equations
(x1,y1)=(−1,−7)(x2,y2)=(27,2)
Evaluate
{xy=72x−y=5
Solve the equation for y
More Steps
Evaluate
2x−y=5
Move the expression to the right-hand side and change its sign
−y=5−2x
Change the signs on both sides of the equation
y=−5+2x
{xy=7y=−5+2x
Substitute the given value of y into the equation xy=7
x(−5+2x)=7
Expand the expression
More Steps
Evaluate
x(−5+2x)
Apply the distributive property
x(−5)+x×2x
Use the commutative property to reorder the terms
−5x+x×2x
Multiply the terms
More Steps
Evaluate
x×2x
Use the commutative property to reorder the terms
2x×x
Multiply the terms
2x2
−5x+2x2
−5x+2x2=7
Move the expression to the left side
−5x+2x2−7=0
Factor the expression
More Steps
Evaluate
−5x+2x2−7
Reorder the terms
2x2−5x−7
Rewrite the expression
2x2+(−7+2)x−7
Calculate
2x2−7x+2x−7
Rewrite the expression
x×2x−x×7+2x−7
Factor out x from the expression
x(2x−7)+2x−7
Factor out 2x−7 from the expression
(x+1)(2x−7)
(x+1)(2x−7)=0
When the product of factors equals 0,at least one factor is 0
x+1=02x−7=0
Solve the equation for x
More Steps
Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=−12x−7=0
Solve the equation for x
More Steps
Evaluate
2x−7=0
Move the constant to the right-hand side and change its sign
2x=0+7
Removing 0 doesn't change the value,so remove it from the expression
2x=7
Divide both sides
22x=27
Divide the numbers
x=27
x=−1x=27
Calculate
x=−1∪x=27
Rearrange the terms
{x=−1y=−5+2x∪{x=27y=−5+2x
Calculate
More Steps
Evaluate
{x=−1y=−5+2x
Substitute the given value of x into the equation y=−5+2x
y=−5+2(−1)
Simplify the expression
y=−5−2
Calculate
y=−7
Calculate
{x=−1y=−7
{x=−1y=−7∪{x=27y=−5+2x
Calculate
More Steps
Evaluate
{x=27y=−5+2x
Substitute the given value of x into the equation y=−5+2x
y=−5+2×27
Calculate
y=2
Calculate
{x=27y=2
{x=−1y=−7∪{x=27y=2
Check the solution
More Steps
Check the solution
{−(−7)=72(−1)−(−7)=5
Simplify
{7=75=5
Evaluate
true
{x=−1y=−7∪{x=27y=2
Check the solution
More Steps
Check the solution
{27×2=72×27−2=5
Simplify
{7=75=5
Evaluate
true
{x=−1y=−7∪{x=27y=2
Solution
(x1,y1)=(−1,−7)(x2,y2)=(27,2)
Show Solution
Graph
