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:

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

Let's first simplify the second equation. We can divide all terms by 3:

\[
4x - y = 3
\]

Now we have a simpler system of linear equations:

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

Next, let's solve for \( y \) in the second equation:

\[
y = 4x - 3
\]

Now substitute \( y \) from the second equation into the first equation:

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

Distributing the -2:

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

Combine like terms:

\[
-4x + 6 = 2
\]

Subtract 6 from both sides:

\[
-4x = -4
\]

Dividing both sides by -4 gives:

\[
x = 1
\]

Now that we have \( x \), we can substitute it back into the equation for \( y \):

\[
y = 4(1) - 3 = 4 - 3 = 1
\]

Therefore, the point where the two lines intersect is:

\[
(1, 1)
\]

Thus, the complete sentence would read:

When graphed, the two linear equations intersect at the point \( (1, 1) \).