Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
Solve using the Gauss-Jordan method
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(x,y)=(4,−3)
Evaluate
{3x+2y=65x+4y=8
Solve the equation for x
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Evaluate
3x+2y=6
Move the expression to the right-hand side and change its sign
3x=6−2y
Divide both sides
33x=36−2y
Divide the numbers
x=36−2y
{x=36−2y5x+4y=8
Substitute the given value of x into the equation 5x+4y=8
5×36−2y+4y=8
Simplify
35(6−2y)+4y=8
Multiply both sides of the equation by LCD
(35(6−2y)+4y)×3=8×3
Simplify the equation
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Evaluate
(35(6−2y)+4y)×3
Apply the distributive property
35(6−2y)×3+4y×3
Simplify
5(6−2y)+4y×3
Multiply the terms
5(6−2y)+12y
Expand the expression
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Calculate
5(6−2y)
Apply the distributive property
5×6−5×2y
Multiply the numbers
30−5×2y
Multiply the numbers
30−10y
30−10y+12y
Add the terms
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Evaluate
−10y+12y
Collect like terms by calculating the sum or difference of their coefficients
(−10+12)y
Add the numbers
2y
30+2y
30+2y=8×3
Simplify the equation
30+2y=24
Move the constant to the right side
2y=24−30
Subtract the numbers
2y=−6
Divide both sides
22y=2−6
Divide the numbers
y=2−6
Divide the numbers
y=−3
Substitute the given value of y into the equation x=36−2y
x=36−2(−3)
Simplify the expression
x=4
Calculate
{x=4y=−3
Check the solution
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Check the solution
{3×4+2(−3)=65×4+4(−3)=8
Simplify
{6=68=8
Evaluate
true
{x=4y=−3
Solution
(x,y)=(4,−3)
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