To find a solution for the given system of equations:
1. \( -2x + y = -3 \)
2. \( -x + 2y = 3 \)
we can use either the substitution method or the elimination method. Here, we'll use the elimination method.
First, let's multiply the second equation by 2 to make the coefficients of \(y\) the same in both equations:
2. \( -2x + 4y = 6 \)
Let's now write both equations:
1. \( -2x + y = -3 \)
2. \( -2x + 4y = 6 \)
Next, subtract equation 1 from equation 2 to eliminate \(x\):
\[
(-2x + 4y) - (-2x + y) = 6 - (-3)
\]
This simplifies to:
\[
4y - y = 6 + 3
\]
\[
3y = 9
\]
\[
y = 3
\]
Now that we have \(y = 3\), we can substitute \(y\) back into one of the original equations to solve for \(x\). We'll use the first equation:
\[
-2x + y = -3
\]
Substitute \(y = 3\):
\[
-2x + 3 = -3
\]
Subtract 3 from both sides:
\[
-2x = -6
\]
Divide by -2:
\[
x = 3
\]
So the solution to the system of equations is \((x, y) = (3, 3)\).
Therefore, the correct option is:
\[
(3, 3)
\]
7.
Find a solution to the following system of equations.
−2x + y = −3
−x + 2y = 3
(–21, –9)
(3, 3)
(0, 2)
(–3, –9)
1 answer