To solve the given system of equations:
[tex]\[
\begin{cases}
2x + 7y = 3 \\
x = -4y
\end{cases}
\][/tex]
we'll use the method of substitution. Here’s the step-by-step solution:
1. We start with the second equation:
[tex]\[
x = -4y
\][/tex]
2. Substitute the expression for \(x\) from the second equation into the first equation:
[tex]\[
2(-4y) + 7y = 3
\][/tex]
3. Simplify the equation:
[tex]\[
-8y + 7y = 3
\][/tex]
4. Combine like terms:
[tex]\[
-y = 3
\][/tex]
5. Solve for \(y\):
[tex]\[
y = -3
\][/tex]
6. Now substitute the value of \(y\) back into the equation \(x = -4y\) to find \(x\):
[tex]\[
x = -4(-3)
\][/tex]
7. Simplify to find \(x\):
[tex]\[
x = 12
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
x = 12
\][/tex]
[tex]\[
y = -3
\][/tex]
