Question

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?

Answer 1

There are infinitely many solutions; one of which is:

`A = 4, B = -3, and C = -20`

Explanation:

You 2 equations:

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

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

`3(-2)+4(4)=10`

`10=10 larr` verified

We have 2 equations and 3 unknown values; this means that there are an infinite number of values for `A, B and C` 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 = 4` and `B= -3`:

`4x-3y= C`

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

`4(-2)-3(4)= C`

`C = -20`