Certainly! Let's solve the given system of equations step-by-step:
The system of equations given is:
1. [tex]\(4x - 2y = -26\)[/tex]
2. [tex]\(-3x + 6y = 33\)[/tex]
Here's the plan to solve this system:
1. Simplify the equations if possible.
2. Use either the substitution method or the elimination method to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
### Step 1: Simplify the equations
First, observe the given equations. Notice the second equation is:
[tex]\[
-3x + 6y = 33
\][/tex]
If we divide this entire equation by 3, it simplifies to:
[tex]\[
-x + 2y = 11
\][/tex]
So, the system now looks like this:
1. [tex]\(4x - 2y = -26\)[/tex]
2. [tex]\(-x + 2y = 11\)[/tex]
### Step 2: Use the Elimination Method
Next, we'll use the elimination method to eliminate one of the variables. Let's add the two equations together to eliminate [tex]\(y\)[/tex]:
[tex]\[
\begin{array}{c}
(4x - 2y) + (-x + 2y) = -26 + 11 \\
4x - 2y - x + 2y = -15 \\
3x = -15
\end{array}
\][/tex]
Now, solve for [tex]\(x\)[/tex]:
[tex]\[
3x = -15 \implies x = \frac{-15}{3} \implies x = -5
\][/tex]
### Step 3: Substitute [tex]\(x\)[/tex] back into one of the original equations to solve for [tex]\(y\)[/tex]
We can use the simplified second equation for substitution:
[tex]\[
-x + 2y = 11
\][/tex]
Substitute [tex]\(x = -5\)[/tex] into the equation:
[tex]\[
-(-5) + 2y = 11 \implies 5 + 2y = 11
\][/tex]
Now, solve for [tex]\(y\)[/tex]:
[tex]\[
5 + 2y = 11 \implies 2y = 11 - 5 \implies 2y = 6 \implies y = \frac{6}{2} \implies y = 3
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
(x, y) = (-5, 3)
\][/tex]
