Thread: find the values of the coefficients

For what values of the coefficients a and b is (2,-1) the solution to the following linear system?

ax + by = -7
2ax -3by = 1

(Answer: a= -2, b= 3)

I've been taught to find the values of x and y by substitution or elimination, but how do you find the values of the coefficients a and b is (2,-1) as in the above question?

Please help.
Thanks.

Originally Posted by shenton

For what values of the coefficients a and b is (2,-1) the solution to the following linear system?
ax + by = -7
2ax -3by = 1

(Answer: a= -2, b= 3)

I've been taught to find the values of x and y by substitution or elimination, but how do you find the values of the coefficients a and b is (2,-1) as in the above question?
Please help.
Thanks.

Hi,

you know the values of x and y: x = 2 and y = -1.

Plug in these values into your equations:

2a - b = -7
4a + 3b = 1

Now you have a linear system in (a,b) which you can solve as usual.

EB

I never realize I could just plug in those values like that.

This is really an eye opener for me.

Thanks, earboth for showing me how.