Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(−4,−25)(x2,y2)=(5,2)
Evaluate
{xy=10x−2y=1
Solve the equation for x
{xy=10x=1+2y
Substitute the given value of x into the equation xy=10
(1+2y)y=10
Simplify
y(1+2y)=10
Expand the expression
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Evaluate
y(1+2y)
Apply the distributive property
y×1+y×2y
Any expression multiplied by 1 remains the same
y+y×2y
Multiply the terms
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Evaluate
y×2y
Use the commutative property to reorder the terms
2y×y
Multiply the terms
2y2
y+2y2
y+2y2=10
Move the expression to the left side
y+2y2−10=0
Factor the expression
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Evaluate
y+2y2−10
Reorder the terms
2y2+y−10
Rewrite the expression
2y2+(5−4)y−10
Calculate
2y2+5y−4y−10
Rewrite the expression
y×2y+y×5−2×2y−2×5
Factor out y from the expression
y(2y+5)−2×2y−2×5
Factor out −2 from the expression
y(2y+5)−2(2y+5)
Factor out 2y+5 from the expression
(y−2)(2y+5)
(y−2)(2y+5)=0
When the product of factors equals 0,at least one factor is 0
y−2=02y+5=0
Solve the equation for y
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Evaluate
y−2=0
Move the constant to the right-hand side and change its sign
y=0+2
Removing 0 doesn't change the value,so remove it from the expression
y=2
y=22y+5=0
Solve the equation for y
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Evaluate
2y+5=0
Move the constant to the right-hand side and change its sign
2y=0−5
Removing 0 doesn't change the value,so remove it from the expression
2y=−5
Divide both sides
22y=2−5
Divide the numbers
y=2−5
Use b−a=−ba=−ba to rewrite the fraction
y=−25
y=2y=−25
Calculate
y=2∪y=−25
Rearrange the terms
{x=1+2yy=2∪{x=1+2yy=−25
Calculate
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Evaluate
{x=1+2yy=2
Substitute the given value of y into the equation x=1+2y
x=1+2×2
Calculate
x=5
Calculate
{x=5y=2
{x=5y=2∪{x=1+2yy=−25
Calculate
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Evaluate
{x=1+2yy=−25
Substitute the given value of y into the equation x=1+2y
x=1+2(−25)
Calculate
x=−4
Calculate
{x=−4y=−25
{x=5y=2∪{x=−4y=−25
Calculate
{x=−4y=−25∪{x=5y=2
Check the solution
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Check the solution
{−4(−25)=10−4−2(−25)=1
Simplify
{10=101=1
Evaluate
true
{x=−4y=−25∪{x=5y=2
Check the solution
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Check the solution
{5×2=105−2×2=1
Simplify
{10=101=1
Evaluate
true
{x=−4y=−25∪{x=5y=2
Solution
(x1,y1)=(−4,−25)(x2,y2)=(5,2)
Show Solution
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