y is some number and it is equal to -4x+2
y being that same number is also equal to x-3
therefore, we can equate -4x+2 and x-3 to get x-3 = -4x+2
This is the same as starting with y = -4x+2 and replacing the y with x-3
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Let's solve for x
x-3 = -4x+2
x-3+4x = -4x+2+4x .... add 4x to both sides
5x-3 = 2
5x-3+3 = 2+3 .... add 3 to both sides
5x = 5
5x/5 = 5/5 .... divide both sides by 5
x = 1
With this x value, you can now find the y value. Pick any equation that has x and y in it. If we picked the first equation, then
y = -4x+2
y = -4*1+2 ... plug in x = 1
y = -4+2
y = -2
Or we can pick the second equation
y = x-3
y = 1-3 .... plug in x = 1
y = -2
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The solution to the system is (x,y) = (1, -2)
Graphing the two lines will have them intersect at this location.
