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:

System of Equations

We are given the system of equations:

ax - by = 4

bx - ay = 10

And it's known the solutions are: x=2, y=1.

Plugging in the solutions:

2a - b = 4 [1]

2b - a = 10 [2]

Now we have to solve the system above. Multiply [1] by 2:

4a - 2b = 8

Now we add with [2]:

3a = 18

a = 18/3 = 6

a = 6

From [2]:

2b - 6 = 10

2b = 16

b = 16/2 = 8

b = 8

The values are a=6, b=8