Let’s solve the system of linear equations:
[tex]\[
\begin{cases}
y = 2x + 3 \\
y = -x + 9
\end{cases}
\][/tex]
Step 1: Set the two equations equal to each other to find x.
Since both expressions equal [tex]\( y \)[/tex]:
[tex]\[
2x + 3 = -x + 9
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
Add [tex]\( x \)[/tex] to both sides of the equation:
[tex]\[
2x + x + 3 = 9
\][/tex]
Combine like terms:
[tex]\[
3x + 3 = 9
\][/tex]
Subtract 3 from both sides of the equation:
[tex]\[
3x = 6
\][/tex]
Divide both sides by 3:
[tex]\[
x = 2
\][/tex]
Step 3: Substitute [tex]\( x = 2 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex].
Using [tex]\( y = 2x + 3 \)[/tex]:
[tex]\[
y = 2(2) + 3
\][/tex]
Perform the multiplication and addition:
[tex]\[
y = 4 + 3 = 7
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (2, 7)
\][/tex]
Therefore, the solution to the system of equations is [tex]\( x = 2 \)[/tex] and [tex]\( y = 7 \)[/tex].
