Use the image to answer the question.

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
?

(1 point)
The ordered pair (
,
) is the solution to the system of equations because it is the point at which both lines intersect, so both lines share this point.

Answer 1

To find the solution of the system of equations given by \( y = 2x - 1 \) and \( y - 3 = 4x \), we first need to express both equations in a similar format.

1. The first equation is already in slope-intercept form: \[ y = 2x - 1 \]

2. For the second equation, we can rewrite it: \[ y - 3 = 4x \implies y = 4x + 3 \]

Now we can set the two equations equal to each other since they both equal \( y \): \[ 2x - 1 = 4x + 3 \]

Next, we solve for \( x \): \[ 2x - 4x = 3 + 1 \ -2x = 4 \ x = -2 \]

Now that we have \( x = -2 \), we can substitute this back into either equation to find \( y \). Let's use the first equation: \[ y = 2(-2) - 1 \ y = -4 - 1 \ y = -5 \]

Thus, the solution to the system of equations, which represents the point of intersection of the two lines, is: \[ (x, y) = (-2, -5) \]

Therefore, the ordered pair is \((-2, -5)\).