Question

2x = 4y + 8, x - 2y = 4
System of Equations

Answer 1

infinite number of solutions

Explanation:

Given the 2 equations

2x = 4y + 8 → (1)

x - 2y = 4 → (2)

Rearrange (2) making x the subject by adding 2y to both sides

x = 4 + 2y → (3)

Substitute x = 4 + 2y into (1)

2(4 + 2y) = 4y + 8 ← distribute and simplify left side

8 + 4y = 4y + 8

Since both sides are the same this indicates the system has an infinite number of solutions.

one possible solution is, found by choosing a value for y and substituting into (3)

y = 1 : x = 4 + 2(1) = 4 + 2 = 6 , that is

(6, 1 )

Other possible solutions may be generated in the same way.

Answer 2

`y = 2 \\ {0 \: and \:2}`

Explanation:

-2 + 2(3) =-2 +6 = 4 for the 2nd equation

2(-2) + 4(3) = -4 +12 = 8 for the 2nd equation

(-2,3) satisfies both equations

let x = 0, then y= 2 (0,2) is another solution

there's multiple solutions, including (-2,3) and (0,2). That eliminates all answers except the first

Try graphing the two equations. They're the same line, with an infinite number of points on the line, which means an infinite number of solutions.