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
Jan 10, 2018

Answer:

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#