Math CentralQuandaries & Queries


Question from Dushayne, a student:

Please help me in solving this problem:
a. 3x-4y=32

b. 2x+3y=11


The standard technique to use here is to use the two equations to eliminate one of the variables and be left with one equation with one variable. Here is an example

4x + 2y = 5
6x + 8y = 15

What I see here is that if I multiply both sides of the first equation by 4 then the y-term in bath equation will have a coefficient of 8.

16x + 8y = 20
  6x + 8y =15

Subtract the second equation from the first equation to get

10x = 5 so x = 1/2.

Finally substitute x = 1/2 into either of the original equations to find x. I will substitute x = 1/2 into the first equation to get

2 + 2y = 5 so 2y = 3 and y = 3/2.

Thus my answer is x = 1/2, y = 3/2.

Now try your equations,

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