Question

Solve each system by substitution.

1.) 7x+21-23
6x+y= 14

2.) y=-4
y=-3x-10


3.) y=-3x+8
y=5x-16

Answer 1

1) (x, y) = (1, 8)

2) (x, y) =(-2, -4)

3) (x, y) = (3, -1)

Explanation:

1) Given the equations;

7x+2y =23 .... 1

6x+y= 14 .... 2

From 2; y = 14-6x

Substitute into 1;

From 1; 7x+2y =23

7x + 2(14-6x) = 23

7x + 28 - 12x = 23

-5x = 23 - 28

-5x = -5

x = 5/5

x = 1

Substitute x = 1 into y = 14-6x

y = 14 - 6 (1)

y - 14 - 6

y = 8

Hence (x, y) = (1, 8)

2) Given

y=-4

y=-3x-10

We will simply equate bith expression and get x;

-3x - 10 = -4

-3x = -4 + 10

-3x = 6

x = 6/-3

x = -2

Hence the solution is (-2, -4)

3) Given the equation

y=-3x+8

y=5x-16

Equate both expressions;

-3x + 8 = 5x - 16

-3x - 5x = -16 - 8

-8x = -24

x = 24/8

x = 3

Substitute x = 3 into y=-3x+8

y = -3(3) + 8

y = -9 + 8

y = -1

Hence the solution (x, y) = (3, -1)