Solve x+y=8 and 2x+y=11 using substitution
How to solve x+y=8 and 2x+y=11 using substitution
You have a choice whether you want to substitute for x or y. I look at both equations and I notice that the second one has 2x + y, so it might be easier to substitute for y.
In the first equation, let's solve for y. x + y = 8, subtract x from both sides
y = 8-x
Now in the second equation, use (8-x) in place of y: 2x + y =11, so 2x + (8-x) = 11
Solve for x. 2x -x + 8 =11 Combine x terms
x+8 = 11, subtract 8 both sides.
x = 3
Now that you know x =3, substitute that in for x in either equation and solve for y. Once you know BOTH x and y, you have the solution. The coordinate (x,y) represents where the 2 lines will intersect.
Looking at the equation, x+y=8, I can subtract either x or y from both sides to get the following two equations:
x = 8 - y, or y = 8 - x.
So I now have an expression which I can substitute for either x or y.
Now, looking at the equation, 2x + y = 11, I can substitute either way:
2x + y = 11 2x + y = 11
2 (8 - y) + y = 11 2x + (8 - x) = 11
16 - 2y + y = 11 2x + 8 - x = 11
-2y + y = 11 - 16 2x - x = 11 - 8
-y = -5 therefore y = 5 x = 3
Now, to check our work: x + y = 3 + 5 = 8
and: 2x + y = (2 * 3) + 5 = 6 + 5 = 11.