Question

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 can first rewrite the second equation in slope-intercept form.

Starting with the second equation:
\[
y - 3 = 4x
\]
Add 3 to both sides:
\[
y = 4x + 3
\]

Now we have the two equations:
1. \( y = 2x - 1 \)
2. \( y = 4x + 3 \)

Next, we can set the two equations equal to each other to find the x-coordinate of the intersection point:
\[
2x - 1 = 4x + 3
\]

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

Now substitute \( x = -2 \) back into one of the original equations to find the corresponding \( y \)-coordinate. We will use the first equation:
\[
y = 2(-2) - 1 = -4 - 1 = -5
\]

Thus, the ordered pair (solution to the system of equations) is:
\[
\boxed{(-2, -5)}
\]

So, the ordered pair \((-2, -5)\) is the solution to the system of equations because it is the point at which both lines intersect.