Question

Y = 2x + 4
6x – 3y = -12
System by substitution 10 points

Answer 1

Infinitely many solutions

Explanation:

`y=2x+4\\ [2] 6x-3y=-12` < ------------- Linear equations given

Equations Simplified or Rearranged :

`y - 2x = 4 \\ [2] -3y + 6x = -12`

Solve by Substitution :

// Solve equation [1] for the variable
`y`

`[1] y = 2x + 4`

// Plug this in for variable
`y` in equation
`[2]`

`[2] -3*(2x+4) + 6x = -12`

[2]
`0 = 0 =>` Infinitely many solutions

Answer 2

(-2, 0)

Explanation:

y = 2x+4

6x - 3y = -12

Start by simplifying the second equation by dividing everything by 3 (this will make the math easier)...

2x - y = -4

Then, substitute 2x+4 for y into the second equation (this is because y = 2x+4)...

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

Distribute the -3

2x-3(2x)-3(4)=-4

2x-6x-12=-4

Combine like terms

-4x-12=-4

Add 12 to both sides

-4x-12+12=-4+12

-4x=8

Divide both sides by -4

x=-2

Plug -2 back in for x to solve for y:

y = 2(-2) + 4

y=-4+4

y=0

(x, y) = (-2, 0)