SOLUTION: i need your help in solving this equation: using comparion method y=2x-3 y=-1/2x+4 and this one using substitution method x-2y=3 2x-3y=y thank you so much, ana

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: i need your help in solving this equation: using comparion method y=2x-3 y=-1/2x+4 and this one using substitution method x-2y=3 2x-3y=y thank you so much, ana       Log On


   

Question 424971: i need your help in solving this equation: using comparion method
y=2x-3
y=-1/2x+4
and this one using substitution method
x-2y=3
2x-3y=y
thank you so much, ana
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=2x-3.....1...
y=-%281%2F2%29x%2B4....2
first multiply second equation by 4 then add 1 and 2

y=2x-3.....1...
4y=4%28-1%2F2%29x%2B4%2A4....2

y=2x-3.....1...
4y=cross%284%292%28-1%2Fcross%282%29%29x%2B16....2
y=2x-3.....1...
4y=-2x%2B16....2
------------------------ now add them
y%2B4y=2x%2B%28-2x%29-3%2B16
5y=cross%282x%29%2Bcross%28%28-2x%29%29-3%2B16

5y=13}
y=13%2F5
y=2.6....now find x

y=2x-3.....1...
2.6%2B3=2x
5.6=2x
5.6%2F2=+x
2.8=+x

check:
4y=-2x%2B16....2
4%2A2.6=-2%2A2.8%2B16
10.4+=+-5.6%2B16
10.4+=+10.4

2.

using substitution method
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+-2%5Cy+=+3%2C%0D%0A++++2%5Cx+%2B+-4%5Cy+=+0+%29%0D%0A++We'll use substitution. After moving -2*y to the right, we get:
1%2Ax+=+3+-+-2%2Ay, or x+=+3%2F1+-+-2%2Ay%2F1. Substitute that
into another equation:
2%2A%283%2F1+-+-2%2Ay%2F1%29+%2B+-4%5Cy+=+0 and simplify: So, we know that y=6=0. Since x+=+3%2F1+-+-2%2Ay%2F1, x=15.

Answer: system%28+x=15%2C+y=6=0+%29.