SOLUTION: Please help me with the following: Solve by substitution x + y = 12 y = 2x Solve by addition 5x - 3y = 13 4x - 3y = 11

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Please help me with the following: Solve by substitution x + y = 12 y = 2x Solve by addition 5x - 3y = 13 4x - 3y = 11       Log On


   

Question 123099: Please help me with the following:
Solve by substitution x + y = 12
y = 2x
Solve by addition 5x - 3y = 13
4x - 3y = 11

Answer by johnnico6426(16) About Me  (Show Source):
You can put this solution on YOUR website!
Substitution:
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+12%2C%0D%0A++++-2%5Cx+%2B+1%5Cy+=+0+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+12+-+1%2Ay, or x+=+12%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
-2%2A%2812%2F1+-+1%2Ay%2F1%29+%2B+1%5Cy+=+0 and simplify: So, we know that y=8. Since x+=+12%2F1+-+1%2Ay%2F1, x=4.

Answer: system%28+x=4%2C+y=8+%29.


Addition:
5x - 3y = 13
4x - 3y = 11
Multiply the top part with -4 and the buttom with 5
-20x + 12y = -52
20x - 15y = 55
You add them down
-3y = 3
Solve for y.
y=-1
Subsitute y=3 for the y in either the first and second equation. Solve for x. You should get x=2. The solution should be (2, -1)