Solution Sets of Simultaneous Equations Practice

Question

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Question
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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.
Remaining Attempts : 3
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Answer 1

To find the solution to the system of equations given by \( y = 2x - 1 \) and \( y - 3 = 4x \), we can solve them simultaneously.

First, let's rewrite the second equation in slope-intercept form:

1. Start with the equation: \[ y - 3 = 4x \] 2. Add 3 to both sides: \[ y = 4x + 3 \]

Now we have two equations to work with:

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

Since both equations equal \( y \), we can set them equal to each other:

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

Next, let's 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 \( x \), we can substitute it back into one of the original equations to find \( y \). Let's use \( y = 2x - 1 \):

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

Calculating that:

\[ y = -4 - 1 = -5 \]

Thus, the solution to the system of equations is:

\((x, y) = (-2, -5)\)

So, the ordered pair is:

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