To solve the given system of equations, we need to find the point [tex]\((x, y)\)[/tex] that satisfies both equations simultaneously. The given equations are:
[tex]\[
\begin{array}{l}
y = -3x + 6 \\
y = 2x - 4
\end{array}
\][/tex]
To find the solution, follow these steps:
1. Set the equations equal to each other because both expressions on the right-hand side are equal to [tex]\(y\)[/tex]. Therefore, we can write:
[tex]\[
-3x + 6 = 2x - 4
\][/tex]
2. Combine like terms to isolate [tex]\(x\)[/tex]. Move all [tex]\(x\)[/tex]-terms to one side of the equation and the constant terms to the other side:
[tex]\[
-3x + 6 = 2x - 4
\][/tex]
First, we subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[
-3x - 2x + 6 = -4
\][/tex]
[tex]\[
-5x + 6 = -4
\][/tex]
Next, we subtract 6 from both sides:
[tex]\[
-5x = -4 - 6
\][/tex]
[tex]\[
-5x = -10
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(-5\)[/tex]:
[tex]\[
x = \frac{-10}{-5}
\][/tex]
[tex]\[
x = 2
\][/tex]
4. Substitute [tex]\(x\)[/tex] back into one of the original equations to find the value of [tex]\(y\)[/tex]. We'll use the first equation [tex]\(y = -3x + 6\)[/tex]:
[tex]\[
y = -3(2) + 6
\][/tex]
[tex]\[
y = -6 + 6
\][/tex]
[tex]\[
y = 0
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
\boxed{(2, 0)}
\][/tex]
