Homework Help

[diehljen]

I need some help on a homework problem. I am working on the chapter, System of Equations, and one of the questions is: Solve graphically and then determine which statement below describes the system 3x+y=5
x-2y=4
a. The lines intersect and the sysyem has one solution whose x coordinate is x=2
b. The lines intersect and the system has one solution whose y coordinate is y=1
c. The lines intersect and the system has one solution whose y coordinate is y=-2
d. The lines are parallel and the system is inconsistent.

I have no idea how to solve the problem and the steps that are given by the book and our math workshop website are very confusing and make no sense... any help?

thanks!

 

[Loren]

The first thing you have to do is graph the system. Each of these equations will form a straight line. These lines will either be parallel or they intersect or one is on top of the other. If they intersect, you have one solution which consists of the x and y values of the point of intersection. For instance, if the lines intersect at (5,-3), the x value of the solution of the system is +5 and the y value of the solution of the system is -3. This means that if you replace the x's in the original equations with 5 and replace the y's in the original equations with '3, both equations will tell the truth. If the lines are parallel, the system has no real solution. If the lines are colinear, the system has an infinite number of solutions.

 

[mmm4444bot]

Do you know how to graph lines, given their equations?

The exercise tells you to "Solve graphically". So, you must start by graphing each of the following lines on the same set of xy-axis.

3x + y = 5

x - 2y = 4

You're looking to see if these two lines intersect.

Use graph paper!

 

[garf]

Hi!
This may help:
the equation x-2y=4
-2y=4-x
y=(4/(-2))-(x/(-2))
y= -2 + (x/2)
If you choose x= 2 then y=-1
If x=4 then y=0
So you have the pairs: (2,-1), (4,0)
Graph this two points and you have one of the lines (connect the dots)
Do the same to the other line and you have both lines and will know if they intersect and where,
garf