Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
(x,y)≈(1.327464,0.567485)
Evaluate
{3x2y=11y2x−3y11y2x−3y=3
Solve the equation for x
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Evaluate
11y2x−3y=3
Move the expression to the right-hand side and change its sign
11y2x=3+3y
Divide both sides
11y211y2x=11y23+3y
Divide the numbers
x=11y23+3y
{3x2y=11y2x−3yx=11y23+3y
Substitute the given value of x into the equation 3x2y=11y2x−3y
3(11y23+3y)2y=11y2×11y23+3y−3y
Simplify
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Evaluate
3(11y23+3y)2y
Multiply the terms
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Evaluate
(11y23+3y)2y
Rewrite the expression
121y432(1+y)2×y
Reduce the fraction
121y332(1+y)2×1
Any expression multiplied by 1 remains the same
121y39+18y+9y2
3×121y39+18y+9y2
Multiply the terms
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Multiply the terms
121y39+18y+9y2×3
Multiply the terms
121y3(9+18y+9y2)×3
Multiply the terms
121y33(9+18y+9y2)
121y33(9+18y+9y2)
121y33(9+18y+9y2)=11y2×11y23+3y−3y
Simplify
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Evaluate
11y2×11y23+3y−3y
Multiply the terms
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Multiply the terms
11y2×11y23+3y
Cancel out the common factor 11
y2×y23+3y
Cancel out the common factor y2
1×(3+3y)
Multiply the terms
3+3y
3+3y−3y
The sum of two opposites equals 0
More Steps
Evaluate
3y−3y
Collect like terms
(3−3)y
Add the coefficients
0×y
Calculate
0
3+0
Remove 0
3
121y33(9+18y+9y2)=3
Cross multiply
3(9+18y+9y2)=121y3×3
Simplify the equation
3(9+18y+9y2)=363y3
Rewrite the expression
3(9+18y+9y2)=3×121y3
Evaluate
9+18y+9y2=121y3
Move the expression to the left side
9+18y+9y2−121y3=0
Calculate
y≈0.567485
Substitute the given value of y into the equation x=11y23+3y
x=11×0.56748523+3×0.567485
Calculate
x≈1.327464
Calculate
{x≈1.327464y≈0.567485
Check the solution
{x≈1.327464y≈0.567485
Solution
(x,y)≈(1.327464,0.567485)
Show Solution
