Question

Use the substitution method to determine the solution to the system of equations below. y-2x+2=1 6x - 3y = 3​

Answer 1

Answer: this solution has infinite solutions

Explanation:

original system:

y-2x+2 = 1

6x-3y = 3

Move 2 to right side of equation

y -2x = -1

-3y+6x = 3

solve for y in first equation

⇒ y = 2x - 1

insert y into second equation

⇒ -3(2x-1) + 6x = 3

simplify

⇒ -6x+3+6x = 3

simplify once more

⇒ 3 = 3

this solution has infinite solutions

Answer 2

y = 2x - 1

Explanation:

y - 2x + 2 = 1

6x - 3y = 3​

`y - 2x + 2 = 1 \\ +2x - 2 +2x - 2\\y = 2x - 1`

Plug in for y:

6x - 3(2x - 1) = 3​

6x - 6x + 3 = 3

Simplified, 3 = 3