Question

Solve the system 3x + 4y = 8 and y = 3/4x — 2 using any method. Classify the system.

Answer 1

3x +4y = 8

y = 3/4x - 2

Substitution Method

3x + 4(3/4x -2) = 8

Distributive Property:

3x + 3x -8 = 8

Simplify:

6x -8 = 8

Add 8 to each side:

6x = 16

Divide both sides by 6"

x = 16/6

x = 2 2/3

Now replace x with that and solve for y:

y = 3/4(2 2/3) - 2

y = 2-2 = 0

y=0

Answer 2

The solution is x=8/3 y=0

Explanation:

3x+4y =8

y = 3/4x -2

We will use substitution since the second equation is already solved for y

Substitute the second equation into the first

3x+4(3/4x-2) = 8

Distribute the 4

3x +3x -8 = 8

6x -8 = 8

Add 8 to each side

6x -8+8 = 8+8

6x = 16

Divide by 6

6x/6 = 16/6

x = 8/3

Now we need to find y

y = 3/4 x -2

Substitute x=8/3

y = 3/4 (8/3) -2

y = 8/4 -2

y =2-2

y=0

The solution is x=8/3 y=0