x=-4y+15 x=-5y+20 Substitution

Question

Solve the systems of equations using substitution.Give your solution  the systems as a pair or coordinates. simple solutions©

Answer 1

It is very easy to solve a substitution when both equations start with a variable isolated, in this case x.

x = -4y + 15
and
x = -5y + 20

 

Since we are looking for the one point where these points have the same coordinates (x,y) let's start with the fact they are both equal, at that point, to the same value x.

So, -4y + 15 = x = -5y + 20
-4y + 15 = -5y + 20

 

Now isolate the variable y by adding 5y - 15 to both sides
-4y + 15 + 5y - 15 = -5y + 20 + 5y - 15
y = 5

now, substitute that value of y back into either equation
x = -4(5) + 15 = -20 + 15 = -5

so the coordinates of the intersection of the two lines is (-5,5)

 

Check your our work by substituting those values into the other equation

(-5)= -5(5) + 20 = -25 + 20 = -5   So, it checks out.