# solve system of equations graphically

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• Jun 12th 2008, 08:45 PM
nipun
solve system of equations graphically
solve system of equations graphically

4x+3y=12
4x-y=4

can anybody show me the easy way to do this example.

please answer this question as soon as possible.
• Jun 12th 2008, 08:57 PM
Jhevon
Quote:

Originally Posted by nipun
solve system of equations graphically

4x+3y=12
4x-y=4

can anybody show me the easy way to do this example.

please answer this question as soon as possible.

we have the equations of two lines here. we can find the solution graphically by graphing both lines and seeing where they intersect. if they intersect, the x-coordinate of the point of intersection is the x-value for the solution and the y-coordinate of the point of intersection is the y-value of the solution. if the lines don't intersect, you have no solution. if the lines are in fact the same line (not the case here) then you have an infinite number of intersecting points and hence an infinite amount of solutions
• Jun 12th 2008, 09:02 PM
nipun
you have to graph
solving the systems of equations graphically

4x+3y=12
4x-y=4

can anybody show me how to graph this equations
• Jun 12th 2008, 09:07 PM
Jhevon
Quote:

Originally Posted by nipun
solving the systems of equations graphically

4x+3y=12
4x-y=4

can anybody show me how to graph this equations

no need to repost the question...

why didn't you say you had a problem with graphing in the first place?

for this problem, you will need graphing paper, you need a grid to be "accurate" here.

start with one line, just plot two points. the x and y intercepts are usually good choices, do you know how to find those?

otherwise, just plug in two reasonable x-values and solve for y. this will give you two points. plot them on the graph paper, then take a ruler and draw a straight line through both points. that's it

can you continue?
• Jun 12th 2008, 09:14 PM
nipun
how to find x and y?
• Jun 12th 2008, 09:43 PM
Jhevon
Quote:

Originally Posted by nipun
how to find x and y?

like i said, you can find the x and y intercepts (to find the x-intercept, let y = 0 and solve for x, to find the y-intercept, let x = 0 and solve for y), this will give you two points to plot. otherwise just choose two random (reasonable) values for x. like x = 0 and x = 1, or x = 1 and x = 2, etc. then solve for y for each corresponding x-value.

for example, in the first equation.

4x + 3y = 12

for x-int:

4x + 3(0) = 12

=> 4x = 12

=> x = 3

so the x-intercept is (3,0) and that is one point to plot

for the y-int:

4(0) + 3y = 12

=> 3y = 12

=> y = 4

so (0,4) is the y-intercept which is another point to plot.

so you can plot those two points on graph paper and draw a straight line through them with the aid of a straight edge. do a similar thing for the other line
• Jun 13th 2008, 08:16 AM
masters
Quote:

Originally Posted by Jhevon
like i said, you can find the x and y intercepts (to find the x-intercept, let y = 0 and solve for x, to find the y-intercept, let x = 0 and solve for y), this will give you two points to plot.

for example, in the first equation.

4x + 3y = 12

for x-int:

4x + 3(0) = 12
=> 4x = 12
=> x = 3

so the x-intercept is (3,0) and that is one point to plot

for the y-int:
4(0) + 3y = 12
=> 3y = 12
=> y = 4

so (0,4) is the y-intercept which is another point to plot.

so you can plot those two points on graph paper and draw a straight line through them with the aid of a straight edge. do a similar thing for the other line

Given this info from Jhevon about how to find the x and y intercepts, you should be able to plot both lines. Also be careful about the accuracy of your plots. When solving graphically, it's nice if the intersection falls on integral points. They don't in this case. To check, simply plug the intersection point into both equations and verify they satisify both of them. I've sketched a plot for you on this one. See what you think, and then try some more on your own.