Question

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y = -x + 5
y = x - 3

a) one solution; (1, 4)
b) infinitely many
c) no solution
d) one solution; (4, 1)

Answer 1

Answer:

  d)  one solution; (4, 1)

Step-by-step explanation:

It often works well to follow problem directions. A graph is attached, showing the one solution to be (4, 1).

_____

You know there will be one solution because the lines have different slopes. Each is in the form ...

  y = mx + b

where m is the slope and b is the y-intercept.

The first line has slope -1 and y-intercept +5; the second line has slope 1 and y-intercept -3. The slope is the number of units of "rise" for each unit of "run", so it can be convenient to graph these by starting at the y-intercept and plotting points with those rise and run from the point you know.