Question

Solve the linear system.
3x+2y=85x+2y=12

Answer 1

To solve the given linear system, we first need to write the equations clearly. The equations appear to be:

1. \( 3x + 2y = 8 \)
2. \( 5x + 2y = 12 \)

We can solve this system using the elimination or substitution method. I'll use the elimination method here.

Step 1: Subtract the first equation from the second to eliminate \( y \):

\[
(5x + 2y) - (3x + 2y) = 12 - 8
\]

This simplifies to:

\[
5x - 3x + 2y - 2y = 4
\]

So we have:

\[
2x = 4
\]

Step 2: Solve for \( x \):

\[
x = \frac{4}{2} = 2
\]

Step 3: Substitute \( x = 2 \) back into either of the original equations to find \( y \). We can use the first equation, \( 3x + 2y = 8 \):

\[
3(2) + 2y = 8
\]

This simplifies to:

\[
6 + 2y = 8
\]

Step 4: Solve for \( y \):

\[
2y = 8 - 6
\]
\[
2y = 2
\]
\[
y = 1
\]

So the solution to the system of equations is:

\[
x = 2, \quad y = 1
\]

In ordered pair notation, the solution is:

\[
(2, 1)
\]