Simultaneous equations

5x + 3y = 22
4x - 7y = -20

I find this near impossible
thanks

Hi Daniel,

What I want to do is to use the two equations you have to produce one equation in one unknown which I can solve. In other words I want to either eliminate the x terms or eliminate the y terms. I am going to eliminate the y terms.

In the first equation the coefficient of y is 3 and in the second equation the coefficient of y is -7. Hence if I multiply the first equation by 3 the coefficient of y will be 21, and if I multiply the second equation by 3 the coefficient of y will be -21. If I then add the two equations the y terms will disappear.

5x + 3y = 22
4x - 7y = -20

Multiply the first equation by 7 and the second by 3

7 (5x + 3y) = 7 22
3 (4x - 7y) = -3 20

so

35x + 21y = 154
12x - 21y = -60

Add the two equations to get

47x = 94 and hence x = 2.

If you now substitute x = 2 into the first equation you get

5 2 + 3y = 22
3y = 12
y = 4.

Penny