Question

Solve the system using substitution. Show all work.

y = x - 5
3x - y = 7

Solve the system using the Linear Combination Method. Show all work.

2x + 2y = 12
3x + y = 2

Answer 1

Explanation:

y = x - 5 ← x - 5 can be subbed for y in the second equation, as shown:

3x - y = 7 → 3x - (x - 5) = 7, or 2x + 5 = 7, or 2x = 2, or x = 1.

Subbing 1 for x in the first equation, we get y = 1 - 5 = -4,

and so the solution is (1, -4).

Second system:

2x + 2y = 12

3x + y = 2

Let's eliminate y first. Mult. the 2nd equation by -2, obtaining:

2x + 2y = 12

-6x - 2y = -4

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-4x = 8, and so x = -2. Subbing -2 for x in the 2nd equation, we get:

3(-2) + y = 2, or -6 + y = 2, or y = 8

Then the solution to the second system of equations is (-2, 8).