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Solve system equations 9x+4y=6 and -3x-8y=18

User DrKaoliN
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2 votes

Answer:

(2, -3)

Explanation:

Pick either equation and solve it for either variable.

Then substitute the expression you get into the other equation.

I choose to solve -3x - 8y = 18 for x. Add 3x to both sides, and subtract 18 from both sides to get:

3x = -8y -18 Then divide by 3:

x = (-8/3)y - 6

Now we have "x = something" that we can plug into the other equation:

9x + 4y = 6 Put in the expression we found for x:

9(-8/3(y) - 6) + 4y = 6 Do the multiplication:

-24y - 54 + 4y = 6 Combine the y terms:

-20y - 54 = 6 Add 20y to both sides and subtract 6:

-54 - 6 = 20y

20y = -60 --> y = -3

Now that you know what y is, plug it into either equation and solve for x. Let's put it in the first equation:

9x + 4(-3) = 6

9x - 12 = 6

9x = 18

x = 2

Test if the answer (2, -3) works in either equation:

9x + 4y = 6 Substitute what we calculated:

9(2) + 4(-3) = 6

18 - 12 = 6

And that's true, 18 minus 12 does equal 6, so our answer checks out.

User Finkelson
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