Question

Use graphing methods to find solutions for these systems of linear equations.
a. x-y = -10 and x+y = 0
b.6x+y = 9 and 4x - y = 11
c.2x+y = 12 and -5x + 5y = 15

Answer 1

The solution to the system is the set of points, (x,y) that satisfy both equations simultaneously. This occurs, graphically, when the lines intersect.

I'll help you with (a) and the rest will follow.

To find solutions graphically, you have to be pretty careful with your plotting, so draw everything up neatly and with straight edge/ruler.

To plot a line, all you need are two points. For you first equation,

x-y=-10

when x = 0, -y = -10 ... that is, y = 10. So one of your points for the first line will be (0,10).

Now, when y = 0, x = -10, so your second point for this line will be (-10,0). Plot these two points and draw the line connecting them.

Yo do something similar for the second equation, x+y=0.

When x = 0, y = y = 0 --> (0,0)
When x = 1, y = -1 --> (1,-1)

are two points for the second line. Plot this line.

Now, where the two lines intersect, you have the point, (x,y) that they both share; that is, at this point, for the given x, they generate the same y-value. You need to read off the x- and y-values from your plot.

That's it :)

Answer 2

The plot for the first set should look like this.

Answer 3

You can read off from the plot that (-5,5) is the point of intersection, so x=-5, y=5 solves the first pair of simultaneous equations.

Answer 4

okay, this is a lot

Answer 5

but thanks :)

Answer 6

np