Highschool math

Question

Solve the following system of equations graphically on the set of axes below. (Graph) y=-x+5 and y=2x-1

Answer 1

1) Let's first identify the slope and y-intercept from each equation by using the equation below.

y = mx + b

m is the slope

b is the y-intercept

For the first equation, y = -x + 5, m would be -1 and b would be +5

For the second equation, y = 2x - 1, m would be +2 and b would be -1

2) Let's take a look at what this means in terms of graphing it

Slope = Rise / Run

For the first equation, with a slope of -1, this would be mean we have a -1 rise and then a +1 run

Slope = Rise / Run

-1 = -1 / 1

For the second equation, with a slope of +2, this would mean we have a +2 rise and then a +1 run.

Slope = Rise / Run

+2 = +2 / +1

3) Now let's start drawing the line for the first equation on the graph

For the first equation, with a y-intercept of +5, we would start drawing the graph by placing a dot on the vertical y axis at +5. With a slope of -1, indicating a -1 rise and a +1 run, we would go down one and then over one on the graph, and then place a dot on this spot. Then repeat this about four more times until you have a dot on the x-axis. You can now draw a line connecting the dots starting at the y-intercept of +5 and then goings down and to the right until it crosses the x-axis.

4) Let's now draw the line for the second equation on the graph

For the second equation, with a y-intercept of -1, we would start drawing the graph by placing a dot on the vertical y axis at -1. With a slope of +2, indicating a +2 rise and a +1 run, we would go up two and then over one on the graph, and then place a dot on this spot. Then repeat this about three more times. You can now draw a line connecting the dots starting at the y-intercept of -1 and then going up and to the right until it crosses the first line you drew.

5) We are now ready to solve the system of equations

The point at which the two lines you drew cross each other, or intersect, is the solution to the systems of equations. This point contains both an x coordinate and a y coordinate. The x coordinate is found by drawing an imaginary line from that point down to the horizontal x-axis. The y coordinate is found by drawing an imaginary line form that point over to the vertical y-axis. x is therefore equal to +2 and y is equal to +3.