Solving system of equations

[raristy]

Please help me find a solution so I can guide my son. I will not solve it for him, but can raise a red flag if I see him go on the wrong direction.
Find all values

for which there exists an ordered pair

satisfying the following system of equations:

List only the values for

Thanks a lot.

 

[skeeter]

adding the two equations term for term ...

$2a = 8b \implies b = \dfrac{a}{4}$

substitute $\dfrac{a}{4}$ for $b$ in either equation, then solve for $a$ ... you should get three distinct solutions for $a$ (and $b$)

 

[raristy]

Is it -12,0,12?

 

[skeeter]

Is it -12,0,12?

substitute them back into the original equations and check for yourself ...

 

[raristy]

I did prior to sending the second post and it worked . I've been trying to help him on this but I myself didn't see it until you guided me. I have the eureka! feeling.