Find the values for A, B, and C so that the system will have the solution (-2,4)?

Consider the following system of equations:
3x + 4y =10
Ax + By = C

How did you arrive at your answer?

1 Answer
Douglas K.
Jan 10, 2018

There are infinitely many solutions; one of which is:

A = 4, B = -3, and C = -20A=4,B=−3,andC=−20

Explanation:

You 2 equations:

"1. " 3x+4y=101. 3x+4y=10
"2. " Ax+By=C2. Ax+By=C

We are given that x = -2x=−2 and y = 4y=4; verify that the line for equation 1. contains this point:

3(-2)+4(4)=103(−2)+4(4)=10

10=10 larr10=10← verified

We have 2 equations and 3 unknown values; this means that there are an infinite number of values for A, B and CA,BandC and we are free to choose a solution.

I shall choose a solution so that the line for equation is 2. is perpendicular to the line for equation 1; A = 4A=4 and B= -3B=−3:

4x-3y= C4x−3y=C

To find the value of C, substitute x = -2x=−2 and y = 4y=4:

4(-2)-3(4)= C4(−2)−3(4)=C

C = -20C=−20

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