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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
?

Answer 1

To find the solution for the equations $y=2x-1$ and $y-3=4x$, we will first rewrite the second equation in slope-intercept form (i.e., $y=mx+b$).

Starting with the equation $y-3=4x$:

$$y=4x+3$$

Now we have the two equations:

1. $y=2x-1$
2. $y=4x+3$

Next, we set them equal to each other to find the point of intersection:

$$2x-1=4x+3$$

Now, solve for $x$:

1. Subtract $2x$ from both sides:

$$-1=2x+3$$

2. Subtract 3 from both sides:

$$-1-3=2x$$ $$-4=2x$$

3. Divide by 2:

$$x=-2$$

Now, substitute $x=-2$ back into one of the original equations to find $y$. We can use the first equation $y=2x-1$:

$$y=2(-2)-1$$ $$y=-4-1$$ $$y=-5$$

Therefore, the solution (point of intersection) of the two lines is:

$$\boxed{{\displaystyle (-2,-5)}}$$