Question

Solving System of Equations Using Substitution

Answer 1

1. (x, y) = (-2, 4)
2. (x, y) = (10, 18)
3. (x, y) = (1, 3)

Explanation:

You want to solve systems of equations by substitution.

1. y = x +6; y = -x +2
2. y = 2x -2; y = x +8
3. y = -x +4; y = 3x

Substitution

Using substitution to solve a system of equations means substituting an expression or variable in one equation with an equal expression or variable found using the other equation.

Here, all of the equations are of the form "y = ( )", so it is appropriate to use one expression for y to substitute for y in the other equation.

1. y = x +6; y = -x +2

Substituting for y, we have ...

x +6 = -x +2

2x = -4 . . . . . . . . add x-6 to both sides

x = -2 . . . . . . . . . divide by 2

y = -2 +6 = 4 . . . . find y

The solution is (x, y) = (-2, 4).

2. y = 2x -2; y = x +8

Substituting for y, we have ...

2x -2 = x +8

x = 10 . . . . . . . . add 2-x to both sides

y = 10 +8 = 18 . . . . find y

The solution is (x, y) = (10, 18).

3. y = -x +4; y = 3x

Substituting for y, we have ...

-x +4 = 3x

4 = 4x . . . . . . . . . add x

1 = x . . . . . . . . . . divide by 4

y = 3·1 = 3 . . . . . find y

The solution is (x, y) = (1, 3).