Question

15 points to help answer these two questions?

1) How can graphing methods be used to solge a system of linear equations and how can you determine the equations of the two lines by analyzing the graph?

2) Solve this system of equations and explain what method you used to find your solution.
8x-y=-9
4x-3y=-22

Answer 1

1. Graphing can be used to solve a system of equations because the solution to a system of equations is the point of intersection of the two lines.
If you have a graph with two lines and they intersect at one point, that one point is the solution. If you have a graph with two lines and the lines do not touch(parallel lines) there will be no point of intersection and therefore no solution. If you have a graph of two lines and the lines graph on top of each other this means that they have every single point in common and therefore infinitely many solutions.
2. The solution to the system is (-.25, 7)
I solved using elimination method.
8x - y = -9
4x - 3y = -22
Multipliy the second equation by -2 to clear the x's.

8x - y = -9
-8x + 6y = 44
5y = 35
y = 7
Now plug y back into either of the original equations and solve for x.
8x - 7 = -9
8x = -2
x = - 1/4 or -.25
(-.25,7)