Question

find the solution of the system of equations.
$6x + 12y = 36$
$4x - 6y = -4$
answer attempt 1 out of 3
(\boxed{1}, \square)$

Explanation:

Step1: Simplify the equations

First, simplify the first equation \(6x + 12y = 36\) by dividing each term by 6: \(x + 2y = 6\) (Equation 1).
Simplify the second equation \(4x - 6y = -4\) by dividing each term by 2: \(2x - 3y = -2\) (Equation 2).

Step2: Solve Equation 1 for \(x\)

From Equation 1: \(x = 6 - 2y\).

Step3: Substitute \(x\) into Equation 2

Substitute \(x = 6 - 2y\) into Equation 2:
\(2(6 - 2y) - 3y = -2\)
Expand: \(12 - 4y - 3y = -2\)
Combine like terms: \(12 - 7y = -2\)

Step4: Solve for \(y\)

Subtract 12 from both sides: \(-7y = -14\)
Divide by \(-7\): \(y = 2\).

Step5: Substitute \(y = 2\) into \(x = 6 - 2y\)

\(x = 6 - 2(2) = 6 - 4 = 2\).

Answer:

\((2, 2)\)