Question

Solve the system of equations.

\[\begin{aligned}
& -4x+3y = -2
\\\\
& y=x-1
\end{aligned}\]
\[ x=\]
\[ y=\]

Answer 1

To solve the given system of equations, we can substitute the expression for \( y \) from the second equation into the first equation.

The equations are:

\[
-4x + 3y = -2 \quad (1)
\]
\[
y = x - 1 \quad (2)
\]

Substituting equation (2) into equation (1):

\[
-4x + 3(x - 1) = -2
\]

Now, simplify the left side:

\[
-4x + 3x - 3 = -2
\]

Combining like terms gives:

\[
-x - 3 = -2
\]

Now, add 3 to both sides:

\[
-x = 1
\]

Multiplying both sides by -1 yields:

\[
x = -1
\]

Now we can find \( y \) using equation (2):

\[
y = x - 1
\]
\[
y = -1 - 1 = -2
\]

Thus, the solution to the system of equations is:

\[
x = -1
\]
\[
y = -2
\]