To solve the given system of equations by elimination, follow these steps:
### Given Equations
1. [tex]\(-5x - 2y = -12\)[/tex] (Equation 1)
2. [tex]\(3x + 2y = 8\)[/tex] (Equation 2)
### Step 1: Add the equations
Notice that the coefficients of [tex]\(y\)[/tex] in both equations are opposites ([tex]\(-2\)[/tex] and [tex]\(2\)[/tex]), so adding the equations will eliminate [tex]\(y\)[/tex].
[tex]\[
\begin{array}{rl}
(-5x - 2y) + (3x + 2y) &= -12 + 8 \\
-5x + 3x &= -4 \\
-2x &= -4 \\
x &= 2
\end{array}
\][/tex]
### Step 2: Substitute the value of [tex]\(x\)[/tex] back into one of the original equations
Now that we have [tex]\(x = 2\)[/tex], we can substitute this value back into either Equation 1 or Equation 2 to solve for [tex]\(y\)[/tex]. Let's use Equation 2:
[tex]\[
3x + 2y = 8 \\
3(2) + 2y = 8 \\
6 + 2y = 8 \\
2y = 2 \\
y = 1
\][/tex]
### Step 3: Write the solution as an ordered pair
The solution to the system of equations is [tex]\((x, y) = (2, 1)\)[/tex].
So the ordered pair solution is [tex]\((2, 1)\)[/tex].
