Question

Use the image to answer the question.

Four points are plotted on a coordinate plane, forming two intersecting lines.

What is the solution of y=2x−1
and y−3=4x
?

Answer 1

To find the solution for the equations \(y = 2x - 1\) and \(y - 3 = 4x\), we will first rewrite the second equation in slope-intercept form (i.e., \(y = mx + b\)).

Starting with the equation \(y - 3 = 4x\):

\[
y = 4x + 3
\]

Now we have the two equations:

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

Next, we set them equal to each other to find the point of intersection:

\[
2x - 1 = 4x + 3
\]

Now, solve for \(x\):

1. Subtract \(2x\) from both sides:

\[
-1 = 2x + 3
\]

2. Subtract 3 from both sides:

\[
-1 - 3 = 2x
\]
\[
-4 = 2x
\]

3. Divide by 2:

\[
x = -2
\]

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

\[
y = 2(-2) - 1
\]
\[
y = -4 - 1
\]
\[
y = -5
\]

Therefore, the solution (point of intersection) of the two lines is:

\[
\boxed{(-2, -5)}
\]