Question

How many solutions does this system have?

y=-8x+2
y=-8x+5
no solutions
1 solution
2 solutions
infinite solutions

Answer 1

No Solutions

Explanation:

There are 2 ways to solve this.

ALGEBRAIC WAY

1. Write out the equations.
   y = - 8x + 2
   y = - 8x + 5
2. Combine them because they are both equal to y.
   - 8x + 2 = - 8x + 5
3. Add 8x to both sides.
   - 8x + 8x + 2 = - 8 x + 8x + 5
   0x + 2 = 0x + 5
   2 = 5

The number 2 will never equal 5 which means the equation has no valid solutions.

GRAPH WAY

A system of equations can be represented as a graph. The solutions for the equation are the points where the graphs (lines or curves) intersect.

1. Identify the type of graph.
   Linear (y = mx + c)
2. Are the slopes equal?
   Yes
3. Do they have the same y-intercepts?
   Yes: Infinite Solutions
   No: No Solutions

Answer 2

no solutions

Explanation:

y = - 8x + 2 → (1)

y = - 8x + 5 → (2)

substitute y = - 8x + 2 into (2)

- 8x + 2 = - 8x + 5 ( subtract 2 from both sides )

- 8x = - 8x + 3 ( add 8x to both sides )

0 = 3 ← not possible

this indicates the system has no solutions