Question

Find the values of a and b so that the linear system has the given solution.

Given Solution: (2, 1)
Equation 1: ax - by'= 4
Equation 2: bx - ay = 10

Answer 1

The values are a=6, b=8

Explanation:

The following system of equations

ax - by = 4

bx - ay = 10

Has the solution x=2, y=1. Substituting:

2a - b = 4 [1]

2b - a = 10 [2]

Multiply [1] by 2:

4a - 2b = 8

Add with [2]:

3a = 18

a = 18/3 = 6

a = 6

From [1]:

2*6 - b = 4

b = 12 - 4

b = 8

The values are a=6, b=8