Question

2x − 7y = –4
–2x + 10y = –2

Answer 1

To solve the system of equations:

1. \(2x - 7y = -4\) (Equation 1)
2. \(-2x + 10y = -2\) (Equation 2)

We can use the method of elimination or substitution. Here, we'll use elimination.

First, let's add both equations together to eliminate \(x\):

\[
(2x - 7y) + (-2x + 10y) = -4 + (-2)
\]

This simplifies to:

\[
0x + 3y = -6
\]

Which simplifies further to:

\[
3y = -6
\]

Now, divide both sides by 3:

\[
y = -2
\]

Now, we can substitute \(y = -2\) back into one of the original equations to find \(x\). We'll use Equation 1:

\[
2x - 7(-2) = -4
\]

Simplifying this, we get:

\[
2x + 14 = -4
\]

Now, isolate \(x\):

\[
2x = -4 - 14
\]
\[
2x = -18
\]
\[
x = -9
\]

So the solution for the system of equations is:

\[
x = -9, \quad y = -2
\]

Thus, the solution is \((-9, -2)\).