Solving Each System by Substitution..

Question

Y= 8x - 9, Y= 3x - 4

-4x + y = -6 ,-2x + 6y = -14 Please help me?

Answer 1

a).

Substitution method :

The system of equations are y = 8x - 9 and y = 3x -  4.

Substitute y = 8x - 9 in equation 2 : y = 3x -  4.

8x - 9 = 3x -  4

8x - 3x = -  4 + 9

5x = 5

x = 1.

Substitute x = 1 in equation 1 : y = 8x - 9.

y = 8(1) - 9

y = 8 - 9

y = - 1.

The solution of the given system is (x, y) = (1, - 1).

Answer 2

b).

Substitution method :

The system of equations are - 4x + y = - 6 and - 2x + 6y = - 14.

Simplify equation 1:

- 4x + y = - 6

y = 4x - 6.

Substitute y = 4x - 6 in equation 2 : - 2x + 6y = - 14.

- 2x + 6(4x - 6) = - 14

- 2x + 24x - 36 = - 14

22x = - 14 + 36

22x = 22

x = 22/22

x = 1.

Substitute x = 1 in y = 4x - 6.

y = 4(1) - 6

y = 4 - 6

y = - 2.

The solution of the given system is (x, y) = (1, - 2).