Question

Can you help me solve this problem using elimination?

Answer 1

Answer: (-4, -5)

x = -4 and y = -5

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Multiply both sides of the first equation by 6

`-7x+5y = 3\\6(-7x+5y) = 6(3)\\-42x+30y = 18\\`

In short, the first original equation is equivalent to -42x+30y = 18

Now multiply both sides of the second equation by -5 to get

`-8x+6y = 2\\-5(-8x+6y) = -5(2)\\40x-30y = -10\\`

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

`\begin{cases}-42x+30y = 18\\40x-30y = -10\\\end{cases}`

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.

`-7x+5y = 3\\-7(-4)+5y = 3\\28+5y = 3\\5y = 3-28\\5y = -25\\y = -25/5\\y = -5\\`

Since x = -4 and y = -5, we have the ordered pair solution (-4, -5)