Question

10x − 6y = 2
–2x + 3y = 14

Answer 1

To solve the system of equations:

1. \( 10x - 6y = 2 \) (Equation 1)
2. \( -2x + 3y = 14 \) (Equation 2)

We can use the method of substitution or elimination. Here, I will use the elimination method to make it easier.

First, let's multiply Equation 2 by 2 to align the coefficients of \(x\):

\[
2(-2x + 3y) = 2(14)
\]
\[
-4x + 6y = 28 \quad (Equation 3)
\]

Now, we have:
1. \( 10x - 6y = 2 \) (Equation 1)
2. \( -4x + 6y = 28 \) (Equation 3)

Next, we can add Equation 1 and Equation 3:

\[
(10x - 6y) + (-4x + 6y) = 2 + 28
\]
\[
10x - 4x - 6y + 6y = 30
\]
\[
6x = 30
\]

Now, divide by 6:

\[
x = 5
\]

Now that we have \(x\), we can substitute it back into either equation to find \(y\). Let's use Equation 2:

\[
-2(5) + 3y = 14
\]
\[
-10 + 3y = 14
\]
\[
3y = 14 + 10
\]
\[
3y = 24
\]

Now divide by 3:

\[
y = 8
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (5, 8)
\]