Question 282267: I need help solving a linear system problem using linear comblinations. The problem is 7x-4y=-3 and 2x+5y=-7. I got (1,1), but when I use them they don't work right. First I multiplied 5(7x-4y)=5(-3), 35y-20y=-15, 43y=43, y-1.
The next part I multiplied 2(2x+5y)=2(-7), 14x-8y=-6, -14x-35y=49, 43y=43, y=1.
I'm not sure where I need to go with all of this. Please help me.
Found 2 solutions by nyc_function, richwmiller:
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! 7x-4y=-3...Equation A
2x+5y=-7...Equation B
7x - 4y = -3
-4y = -7x - 3
y = (7/4)x + 3/4
Plug this into Equation B to find x.
2x + 5((7/4)x + 3/4) = -7
2x + (35/4)x + 15/4 = -7
2x(4) + 4[(35/4)x + 15/4] = -7(4)
8x + 35x + 3 = -28
43x = -28 - 3
43x = -31
x = -31/43
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Now, plug this value for x into either equations above to find y.
I will use Equation A but you can also use B.
7(-31/43) - 4y = -3
-217/43 - 4y = -3
-4y = -3 + 217/43
y = (-3 + 217/43)/-4
y = -22/43
SOLUTION POINT: (-31/43, -22/43)....This is the answer.
The point (1,1) is not the answer.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! the other tutor showed you the right wayn tosolve it.
Let's see where you went wrong.
5(7x-4y)=5(-3)
35y-20y=-15,
This is where you went wrong. It should be
35x-20y=-15
You changed x to y
Now for the other equation
2(2x+5y)=2(-7)
should be
4x+10y-14
not sure where you got this
14x-8y=-6
or this
-14x-35y=49
I also don't see what you were trying to do by multiplying the first by 5 and the second by 2. I can see multiplying the first by 5 and the second by 4 to remove the y term -20y and +20y
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