Question

Look at the two equations below.
4x-2y=-2
12x-3y=9





Select the answer choice that makes the sentence true.

When graphed, the two linear equations intersect at the point

.

Answer 1

To find the point where the two equations intersect, we can solve the system of equations. The equations are:

1. \(4x - 2y = -2\)
2. \(12x - 3y = 9\)

We can simplify the second equation first by dividing all terms by 3:

\[
4x - y = 3
\]

Now we have the two equations:

1. \(4x - 2y = -2\)
2. \(4x - y = 3\)

Next, we can solve for \(y\) in terms of \(x\) from the second equation:

\[
4x - y = 3 \implies y = 4x - 3
\]

Now, we can substitute this expression for \(y\) back into the first equation:

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

Simplifying this:

\[
4x - 8x + 6 = -2
\]
\[
-4x + 6 = -2
\]
\[
-4x = -2 - 6
\]
\[
-4x = -8
\]
\[
x = 2
\]

Now, substitute \(x = 2\) back into the equation for \(y\):

\[
y = 4(2) - 3 = 8 - 3 = 5
\]

So the intersection point of the two equations is:

\((x, y) = (2, 5)\)

Therefore, when graphed, the two linear equations intersect at the point **(2, 5)**.