To solve the system of equations:
[tex]\[
\begin{aligned}
y &= 6x - 8 \\
y &= 4x + 6
\end{aligned}
\][/tex]
we need to find a common solution [tex]\((x, y)\)[/tex] that satisfies both equations simultaneously.
### Step-by-Step Solution:
1. Set the equations equal to each other:
Since both equations are equal to [tex]\(y\)[/tex], we can set the right-side expressions of both equations equal to each other.
[tex]\[
6x - 8 = 4x + 6
\][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To find the value of [tex]\(x\)[/tex], we start by isolating [tex]\(x\)[/tex] on one side of the equation.
Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[
6x - 4x - 8 = 4x - 4x + 6 \\
2x - 8 = 6
\][/tex]
Then, add 8 to both sides:
[tex]\[
2x - 8 + 8 = 6 + 8 \\
2x = 14
\][/tex]
Finally, divide both sides by 2:
[tex]\[
x = \frac{14}{2} = 7
\][/tex]
3. Substitute [tex]\(x = 7\)[/tex] back into one of the original equations:
We can use either equation to find the value of [tex]\(y\)[/tex]. Let's use the first equation:
[tex]\[
y = 6x - 8
\][/tex]
Substitute [tex]\(x = 7\)[/tex]:
[tex]\[
y = 6(7) - 8 \\
y = 42 - 8 \\
y = 34
\][/tex]
So, the solution to the system of equations is:
[tex]\[
x = 7
\][/tex]
[tex]\[
y = 34
\][/tex]
