Question

Using the substitution method, how to you solve this system of equations: `y= 4x +34 and y = -2x - 26`?

Answer 1

`x=-10 and y=-6`

The point of intersection is `(-10,-6)`

Explanation:

Both equations are given in the form of `y=mx+c` which is the equation of a straight line.

In terms of graphs, by solving this system of equations, you are finding the point of intersection of the two lines.

We know that the value of `y` in each equation is the same,

`color(white)(xxx.xxx)y" "=" "y`
`:. 4x+34 " "=" "-2x-26" "larr` substitute for `y`

`" "4x+2x = -26-34`

`" "x=-10`

Substitute into both equations to check.

`y = 4(-10)+34 = -40+34 =-6`

`y=-2(-10)-26 = 20+26 =-6`