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.