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Solve the system of equations by elimination. Express the solution as an ordered pair.

[tex]\[
\begin{array}{l}
-5x - 2y = -12 \\
3x + 2y = 8
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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].
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