Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(−60,−2)(x2,y2)=(60,2)
Evaluate
{yx=41xy41xy=30
Solve the equation
More Steps
Evaluate
yx=41xy
Rewrite the expression
yx=4xy
Cross multiply
x×4=yxy
Simplify the equation
4x=yxy
Simplify the equation
4x=y2x
Move the expression to the left side
4x−y2x=0
Factor the expression
x(4−y2)=0
Separate the equation into 2 possible cases
x=0∪4−y2=0
Solve the equation
More Steps
Evaluate
4−y2=0
Move the constant to the right-hand side and change its sign
−y2=0−4
Removing 0 doesn't change the value,so remove it from the expression
−y2=−4
Change the signs on both sides of the equation
y2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±4
Simplify the expression
y=±2
Separate the equation into 2 possible cases
y=2∪y=−2
x=0∪y=2∪y=−2
{x=0∪y=2∪y=−241xy=30
Evaluate
{x=041xy=30∪{y=241xy=30∪{y=−241xy=30
Calculate
More Steps
Evaluate
{x=041xy=30
Substitute the given value of x into the equation 41xy=30
41×0×y=30
Any expression multiplied by 0 equals 0
0=30
Calculate
{x∈∅y∈∅
{x∈∅y∈∅∪{y=241xy=30∪{y=−241xy=30
Calculate
More Steps
Evaluate
{y=241xy=30
Substitute the given value of y into the equation 41xy=30
41x×2=30
Multiply the terms
21x=30
Multiply by the reciprocal
21x×2=30×2
Multiply
x=30×2
Multiply
x=60
Calculate
{x=60y=2
{x∈∅y∈∅∪{x=60y=2∪{y=−241xy=30
Calculate
More Steps
Evaluate
{y=−241xy=30
Substitute the given value of y into the equation 41xy=30
41x(−2)=30
Simplify
More Steps
Evaluate
41x(−2)
Rewrite the expression
−41x×2
Multiply the terms
−21x
−21x=30
Change the signs on both sides of the equation
21x=−30
Multiply by the reciprocal
21x×2=−30×2
Multiply
x=−30×2
Multiply
x=−60
Calculate
{x=−60y=−2
{x∈∅y∈∅∪{x=60y=2∪{x=−60y=−2
Rearrange the terms
{x=−60y=−2∪{x=60y=2
Check the solution
More Steps
Check the solution
{−2−60=41(−60)(−2)41(−60)(−2)=30
Simplify
{30=3030=30
Evaluate
true
{x=−60y=−2∪{x=60y=2
Check the solution
More Steps
Check the solution
{260=41×60×241×60×2=30
Simplify
{30=3030=30
Evaluate
true
{x=−60y=−2∪{x=60y=2
Solution
(x1,y1)=(−60,−2)(x2,y2)=(60,2)
Show Solution
