Solve the system of equations.


\[\begin{aligned}
& -4x+7y = 20
\\\\
& y=3x+15
\end{aligned}\]
\[ x=\]
\[ y=\]

1 answer

To solve the system of equations:

\[ \begin{aligned} & -4x + 7y = 20 \quad \text{(1)} \ & y = 3x + 15 \quad \text{(2)} \end{aligned} \]

we will substitute equation (2) into equation (1).

From equation (2), we have:

\[ y = 3x + 15 \]

Now, substitute \(y\) in equation (1):

\[ -4x + 7(3x + 15) = 20 \]

Expanding this gives:

\[ -4x + 21x + 105 = 20 \]

Combining like terms:

\[ 17x + 105 = 20 \]

Now, isolate \(x\) by subtracting 105 from both sides:

\[ 17x = 20 - 105 \] \[ 17x = -85 \]

Dividing both sides by 17:

\[ x = -5 \]

Now, substitute \(x = -5\) back into equation (2) to find \(y\):

\[ y = 3(-5) + 15 \] \[ y = -15 + 15 \] \[ y = 0 \]

Thus, the solution of the system of equations is:

\[ x = -5 \] \[ y = 0 \]