Question

Identify the type of solution for the following system of equations. y = 3x + 8

y = -7 + 3x
infinitely many solutions, no solution, one solution

Answer 1

Answer: No solution

Step 1: Choose which method you would like to use to solve

Though we can solve using either substitution or elimination, we will use substitution for this one

Step 2: Substitute y for y

-7+3x=3x+8

Step 3: Subtract 3x on both sides

-7+3x=3x+8
-3x=-3x
_________
-7=8

Though we would usually use the x value to solve for y, in this case the x values canceled each other out. We are now left with 2 numbers set equal to each other, and this equation is false. Since -7 does not equal 8, the system of equation have no solution.

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Answer 2

No solution

Explanation:

Given the 2 equations

y = 3x + 8 → (1)

y = - 7 + 3x → (2)

Substitute y = 3x + 8 into (2)

3x + 8 = - 7 + 3x ( subtract 8 from both sides )

3x = - 15 + 3x ( subtract 3x from both sides )

0 = - 15 ← not possible

This indicates the system has no solution