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 to the system of equations given by \( y = 2x - 1 \) and \( y - 3 = 4x \), we can rewrite the second equation in slope-intercept form.

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

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

Next, set the two equations equal to each other to find the value of \( x \):
\[
2x - 1 = 4x + 3
\]

Now, solve for \( x \):
1. Subtract \( 2x \) from both sides:
\[
-1 = 2x + 3
\]
2. Subtract 3 from both sides:
\[
-4 = 2x
\]
3. Divide by 2:
\[
x = -2
\]

Now that we have \( x = -2 \), we can substitute it back into one of the original equations to find \( y \). We'll use the first equation:
\[
y = 2(-2) - 1 = -4 - 1 = -5
\]

The solution to the system of equations is the ordered pair \( (-2, -5) \).

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