Question
Solve the system of equations
(x1,y1)=(−1,−30)(x2,y2)=(1,30)
Evaluate
{2x3y=60xy=30
Solve the equation for x
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Evaluate
xy=30
Evaluate
yx=30
Divide both sides
yyx=y30
Divide the numbers
x=y30
{2x3y=60x=y30
Substitute the given value of x into the equation 2x3y=60
2(y30)3y=60
Simplify
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Evaluate
2(y30)3y
Multiply the terms
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Evaluate
(y30)3y
Rewrite the expression
y327000×y
Reduce the fraction
y227000×1
Any expression multiplied by 1 remains the same
y227000
2×y227000
Multiply the terms
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Multiply the terms
y227000×2
Multiply the terms
y227000×2
Multiply the terms
y254000
y254000
y254000=60
Cross multiply
54000=y2×60
Simplify the equation
54000=60y2
Rewrite the expression
60×900=60y2
Evaluate
900=y2
Swap the sides of the equation
y2=900
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±900
Simplify the expression
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Evaluate
900
Write the number in exponential form with the base of 30
302
Reduce the index of the radical and exponent with 2
30
y=±30
Separate the equation into 2 possible cases
y=30∪y=−30
Rearrange the terms
{x=y30y=30∪{x=y30y=−30
Calculate
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Evaluate
{x=y30y=30
Substitute the given value of y into the equation x=y30
x=3030
Calculate
x=1
Calculate
{x=1y=30
{x=1y=30∪{x=y30y=−30
Calculate
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Evaluate
{x=y30y=−30
Substitute the given value of y into the equation x=y30
x=−3030
Simplify the expression
x=−3030
Calculate
x=−1
Calculate
{x=−1y=−30
{x=1y=30∪{x=−1y=−30
Calculate
{x=−1y=−30∪{x=1y=30
Check the solution
More Steps

Check the solution
{2(−1)3(−30)=60−(−30)=30
Simplify
{60=6030=30
Evaluate
true
{x=−1y=−30∪{x=1y=30
Check the solution
More Steps

Check the solution
{2×13×30=601×30=30
Simplify
{60=6030=30
Evaluate
true
{x=−1y=−30∪{x=1y=30
Solution
(x1,y1)=(−1,−30)(x2,y2)=(1,30)
Show Solution
