Sure, let's solve the system of equations step by step:
We have the system of equations:
[tex]\[
\begin{cases}
y = 3x - 5 \\
x - 4y + 2 = 0
\end{cases}
\][/tex]
Step 1: Solve the first equation for [tex]\( y \)[/tex]:
[tex]\[ y = 3x - 5 \][/tex]
Step 2: Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ x - 4(3x - 5) + 2 = 0 \][/tex]
Step 3: Simplify the expression inside the parentheses:
[tex]\[ x - 12x + 20 + 2 = 0 \][/tex]
Step 4: Combine like terms:
[tex]\[ -11x + 22 = 0 \][/tex]
Step 5: Solve for [tex]\( x \)[/tex]:
[tex]\[ -11x = -22 \][/tex]
[tex]\[ x = \frac{-22}{-11} \][/tex]
[tex]\[ x = 2 \][/tex]
Step 6: Substitute [tex]\( x = 2 \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
[tex]\[ y = 3(2) - 5 \][/tex]
[tex]\[ y = 6 - 5 \][/tex]
[tex]\[ y = 1 \][/tex]
So, the solution to the system of equations is:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 1 \][/tex]
Hence, the solution is:
[tex]\[ (x, y) = (2, 1) \][/tex]
