Thread: Intersection of lines

At what point do the two lines whit the equations 7x-3y=13 and y=2x-3 intersect?

This problem is for extra points, that I really need in my algebra II class.

first off.. to find where two lines intersect.. we'll need to solve the system of equations..

You have two equations

7x - 3y = 13
y = 2x - 3

Since you already have the second equation solved for a variable (y in this case).. we can plug that expression into the first equation for y and solve.

7x - 3(2x - 3) = 13
7x - 6x + 9 = 13
x + 9 = 13
x = 4

Now that we have the x-value where they intersect, we'll find the y-value by plugging the x-value into the second equation

y = 2(4) - 3
y = 8 - 3
y = 5


So, they intersect at the point (4, 5).

Another way to find where they both intersect is to...graph them! Get each of the equations in y = form (standard form) and graph them. It's evident they intersect at (4, 5).