Find scalars (i.e., real numbers) 𝑥 and 𝑦 such that

Question

Find scalars (i.e., real numbers)  and  such that

x + 7y = -27

3x - 6y = 27

-2 + 9y =-38

x=

y=

Answer 1

Using Equation 3:

-2 + 9y = -38

9y = -36

y = -4

Using Equation 2:

3x - 6(-4) = 27

3x + 24 = 27

3x = 3

x = 1

Checking the point (1, -4) in Equation 1:

(1) + 7(-4) = -27

1 - 28 = -27

-27 = -27 is true therefore the values of x and y are x = 1 and y = -4