Algebra

Solve the system of equations using substitution.

x + 4y = -5
3x - 8y = 45

When I tried to solve it, I got x=-17 and y=-3. When I plugged these into the first equation, it didn't work out at all. Could someone please show me the steps so I can see where I went wrong? Thank you!

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  1. I doubled the first and added it to the second to get
    5x = 35,
    so x = 7, subbing that back I got y = -3

    those values verify.

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  2. MC-- 7th grade algebra.
    Thanks for your help, Reiny!

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  3. since you need to solve the system of equations by substitution, solve the first equation for x by subtracting 4y from both sides. You will get x = -5 - 4y.
    Next substitute this expression into the x of the 2nd equation to get
    3(-5 - 4y)- 8y =45
    Now use the distributive property to get
    -15 -12y - 8y =45
    simplify to get
    -15 -20y = 45 (when you combine to negatives you get a negative answer)
    add 15 to both sides and you get
    -20y = 60
    divide both sides by -20 to get y = -3.
    Now replace this answer into the first equation or the x = -5 - 4y equation to get x= -5 - 4(-3) = -5 + 12 = 7
    answer (7,-3)

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