Math CentralQuandaries & Queries


Question from leslie, a student:

6x+8y=40 4x+5y=25

Hi Leslie,

The first thing I noticed is that all the coefficients in the first equation are divisible by 2. Thus I can divide both sides of the first equation by 2 and the equations become

3x + 4y = 40
4x + 5y = 25

The next thing I want to do is eliminate one of the variables. What I see is that if I multiply the first equation by 4 the coefficient of x becomes 4 × 3 = 12 and if I multiply the second equation by 3 the coefficient in this equation becomes 12 also. Then if I subtract the two equations the two 12x terms will cancel. Lets do it.

Multiply the first equation by 4 and it becomes

12x + 16y = 160

You can multiply the second equation by 3. After you do subtract the resulting equations. The two 12x terms will cancel and leave you with one equation to solve for y. Once you know y you can substitute its value into either of the two equations you started with to find x.

If you still have difficulties write back and tell us what you did and we will try to help again.


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