Explain how to solve the system of equations by graphing.Determine if the system has one solution,no solution,or infinitely many solutions. 3x+2y=8 AND y=-1/4x-1 in an essay explaning step by step

Answer 1

Hello!

So, what you wanna try to do is to try to make sure all of your equations are in y= mx + b form. While y=-1/4x-1 is in that form, 3x+2y=8 is not. This means we have to try to solve for y.

3x + 2y = 8

-3x -3x

2y= (-3x + 8)

/2 /2

y= -3/2x +4

Now that we have both equations in y=mx +b form we can graph it! Remember that the intercept is where the graph hits at X=0, and slope is rise over run (Rise/Run).

(unfortunately I can't show this step on this discussion, but I would recommend trying Desmos if you are having trouble)

The last step is finding out where the graphs intercept or cross with each other if they don't cross its no solutions, if they do it's one solution, if they are the same line It's infinite solutions.

Answer 2

I can give you some information for writing your essay.

Plot the two equations and look for an intersection point. That will be your one solution. However, if the two lines are parallel, then there will be infinitely many solutions as one of the variables will be a free variable.

Can't tell from the question for the second equation if it is y = (-1/4)x -1 or y = -1/(4x) - 1 or y = -1/(4x-1). That will make a difference in the answer. If x is in the denominator, there is more than on solution.

If the first equation is an asymptote to the second equation, then there are no solutions. This is not the case here.

If the second equation is linear, to solve the system for x, solve for y in the first equation, y = (8-3x)/2, and set it equal to whatever the second equation is. For example:

(8-3x)/2 = -x/4 -1 gives (x,y) = (4,-2) which should be the same as the intersection of the two lines.