Answer: (-4, -5)
x = -4 and y = -5
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Multiply both sides of the first equation by 6
[tex]-7x+5y = 3\\6(-7x+5y) = 6(3)\\-42x+30y = 18\\[/tex]
In short, the first original equation is equivalent to -42x+30y = 18
Now multiply both sides of the second equation by -5 to get
[tex]-8x+6y = 2\\-5(-8x+6y) = -5(2)\\40x-30y = -10\\[/tex]
The second original equation is the same as 40x-30y = -10
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The original system is the same as this one below
[tex]\begin{cases}-42x+30y = 18\\40x-30y = -10\\\end{cases}[/tex]
Add the equations straight down
- -42x+40x becomes -2x
- 30y+(-30y) becomes 0y or just 0. The y terms go away.
- 18 + (-10) becomes 8
We get -2x = 8 which then solves to x = -4.
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Use that x value to find y. You can use any equation that involves x & y in it.
[tex]-7x+5y = 3\\-7(-4)+5y = 3\\28+5y = 3\\5y = 3-28\\5y = -25\\y = -25/5\\y = -5\\[/tex]
Since x = -4 and y = -5, we have the ordered pair solution (-4, -5)
