2. Algebraically find the intersection points of the two lines whose equations are shown below.

Question

4x+3y= -13

y=6x-8

this is systems of linear equations.

Answer 1

4x + 3y = -13

y = 6x - 8

Substitute the value of y in the first equation,

4 x + 3 ( 6 x - 8 ) = -13

4 x + 18 x -24 = -13

22 x = 24 - 13

22 x = 11

x = 11/22 = 1/2

plug the value of x in y = 6x - 8 and find y

y = 6 ( 1/2 ) - 8

= 3 - 8 = - 5

check these values in both equations,

4x + 3y =? -13

4(1/2) + 3 ( - 5 ) = 2 - 15 = -13

for the second equation

y = 6x - 8

y - 6x =? -8

-5 - 6 ( 1/2) = -5 - 3 = -8