Question

Solve the system of equations graphed on the coordinate axes below.
y, equals, minus, one fifth, x, plus, 2
y=
−
5
1
​
x+2
y, equals, one fifth, x, plus, 4
y=
5
1
​
x+4

Answer 1

To solve the system of equations given by:

1. \( y = -\frac{1}{5}x + 2 \)
2. \( y = \frac{1}{5}x + 4 \)

we can set the equations equal to each other since they both equal \( y \):

\[
-\frac{1}{5}x + 2 = \frac{1}{5}x + 4
\]

To eliminate the fractions, we can multiply through by 5:

\[
-1x + 10 = 1x + 20
\]

Now, we'll combine like terms:

\[
10 - 20 = 1x + 1x
\]
\[
-10 = 2x
\]

Now, divide both sides by 2:

\[
x = -5
\]

Now that we have the value of \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the first equation:

\[
y = -\frac{1}{5}(-5) + 2
\]
\[
y = 1 + 2
\]
\[
y = 3
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-5, 3)}
\]

This means that the two lines intersect at the point (-5, 3).