solve the following algebra problem

Question

solve the system by elimination

 

5x - 2y = 3

2x + 3y = 24

Answer 1

When we eliminate, we need to remove one of the variables in order to focus on the other. I suggest we focus on eliminating the y variable as less multiplication tricks are going to be needed:

5x - 2y = 3
2x + 3y = 24

 

If we multiply the first equation by 3 and the second by 2, we will have -6y and 6y respectively. (If we wanted to get rid of the x variable, we would have to multiply the equations by 2 and five respectively with one of them being negative, hence the focus on y here):

 

15x - 6y = 9

4x + 6y = 48

----------------

19x = 57

Isolate x by dividing both sides by 19:

x = 3

 

Now that we have x, we can solve for y and check our answer:

5 * 3 - 2y = 3

15 - 2y = 3

-2y = -12

y = 6

 

2 * 3 + 3 * 6 = 24

6 + 18 = 24

24 = 24