Question

Solve each equation for y=. Without graphing, classify each system as having one solution, no solution, or infinitely many solutions.

x+y=3
y=2x-3

Answer 1

The answer would be y=3, and there is only one solution.

Explanation:

In the first expression, x+y=3, we can rearrange it to get it in terms of x so we can substitute it for x in the second expression.

x+y=3

Subtract y from both sides: x=-y+3

Substitute x=-y+3 into the second expression: y=2(-y+3)+3

Distribute the 2: y=-2y+6+3

Simplify the right side: y=-2y+9

Add 2y to both sides: 3y=9

Divide by 3: y=3

Since there is a single y coordinate, that means that there is only one solution.