Solve the system of linear equations by graphing

Question

Solve the system of linear equations by graphing.

3y+4x=3

x+3y=-6

Answer 1

Hi DaCaya,

You are interested in the ordered pair where these two lines intersect. Do you have a TI-80s series graphing calculator? Either way, first step is to change the form of these equations to: y = mx +b. Thus:

3y + 4x = 3

3y = -4x + 3

y = (-4/3)x +1

x + 3y = -6

3y = -x - 6

y = (-1/3)x - 2

Now, if you have a graphing calculator, enter y=, enter both lines and set window from -10 to 10 for x, -10 to 10 for y. Look at the graph for an idea as to where the lines intersect. Then, go to 2nd-Calc-Intersect. Hit enter twice, then enter a guess for the x-value of your ordered pair. (It should be somewhere around 2-4). The calculator will give you the intersecting point, which is:

x = 3, y = -3

Without the calculator, you will just need to plot points. Assign values of 0,1,2,3 for x and substitute into both equations to get y. You will eventually see the point of intersection at (3, -3). You can also confirm by substituting those values into the original equations for x and y. I hope this helps.

Answer 2

Hi Dacaya C

I note that your question says “solve by graphing”; to easily graph your lines you need two points on each line. It is both easy and straightforward forward to get the x and y intercepts per line then plot your lines on a hand made grid and draw straight lines through them.

Given 3y + 4x = 3

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

When y = 0, x = 3/4, (3/4, 0)

Use the two points above to draw the line 3y + 4x = 3

Given x + 3y = -6

When x = 0, y = -2, (0, -2)

When y = 0, x = -6, (-6, 0)

Use the two points above to draw the line x + 3y = -6

In lieu of using the intercepts you can always make a table of selected x values and their resulting y values and plot those for each line.

When you draw the two lines on the same grid, your grid whether it is on your piece of paper, from a hand held calculator, or online should encompass a range of numbers that can include your intercepts, and yield the point of intersection. A handheld graphing calculator such as a TI84 may require that your lines be in Slope Intercept Form. An online graphing calculator such as Desmos.com will let you enter the lines exactly as they appear in your question but not all graphing calculators accept the same format.

If you don’t have a graphing calculator or the means to graph by hand (as in no paper) you can graph your given lines at desmos.com it is free and easy to use. You can also use desmos.com to confirm the intercepts and the point of intersection.

If you have never used desmos.com when you go there you can type the lines exactly as they appear in your question. Type in 3y + 4x = 3 press return on the next line type in x + 3y = -6 and press return. Desmos will graph both lines on the same grid and you can see the point of intersection and all the intercepts.

Answer 3

Answer 4

x=0 , y=1

x=1, y=-1/3

x=2, y=-5/3

x=3 y=-3

x=-1, y=7/3