Question

The graph shows two lines, A and B.

A coordinate plane is shown with two lines, A and B, graphed. Line A has a slope of negative 1 and crosses the y axis at 5. Line B has a slope of positive 1 and crosses the y axis at 3.

How many solutions are there for the pair of equations for lines A and B? Explain your answer.


http://learn.flvs.net/webdav/assessment_images/educator_mjprealgebra_v16/08_04_01.jpg

Answer 1

Just draw the graph ( I can't open the link) hence draw the graph based on imfo provided and you can see the solution itself. Reply if yo uhave any doubt

Answer 2

I can just attach a file is that alright?

Answer 3

@aadi4502

Answer 4

@MrAnonymous You can see from the graph itself. The no. of points they are intersecting will resemble to no. of solutions they have. In the picture, they are intersecting only at a single point, hence 1 solution

Answer 5

Oh I see. Thanks!

Answer 6

@aadi4502 Can you help with one more?

Answer 7

@MrAnonymous Sure go ahead. :)

Answer 8

Consider the following pair of equations:

y = x + 4
y = −2x − 2

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answer 9

@aadi04502

Answer 10

@MrAnonymous So, you want the solution through substitution method. Well, lets learn the other method first. You can plot the graphs and then see their intersection and find the value of x (where they would intersect). Now, in substitution, take the value of (y) from equation 1 and put into eqn 2.
What do you get.? You get a linear single variable equation in (x) i.e
x+4=-2x-2. Now, you solve for x. Do you want me to solve it? I guess you can solve this buddy on your own. Just try it and get a value of x. Now, this value of x, is the point where these two straight lines intersect. To know the (y) value, put obtained (x) value in any of the two equations. Reply if you have further doubts.

Answer 11

@aadi4502 I'm gonna be honest, I didn't really get much of that. Can you make it a little simpler for me?

Answer 12

Since both equations are equal to y, that means both equations have to be equal to each other, right? Think about it.

Answer 13

@thatonegirl_ I get that but I cannot find the value of x. Can you help me find it?

Answer 14

Ok, @MrAnonymous : Lets go over it again. You are given two equations y=x+4 and y=-2x-2. The question asks to find the solutions of the two lines by substitution method.
First of all, do you know that these two equations represents two different straight lines?.with some slope. (Skipping the slope part).
And if you plot these lines (like the one question above where you plotted them), you would notice that they intersect at some point. Now that point is called the solution of the two equations. It means that the values of (x) and (y) at the solution point will be same for both the equations.
So , in order to find the solution by substitution, you need to substitute the value of (y) from one equation to other one.
From equation 1, the value of (y) is y= x+4.
Now, you replace this value of (y) in the second equation that is, equate it to (y)=-2x-2. So, What was the value of (y), It was x+4 , but value of (y) is also -2x-2. Hence, in order to have a solution, both these values must be equal. Hence, we equate x+4=-2x-2 and solve for (x).
Now, on solving you will get the value of (x) =-2. Putting this value in either of the two equations, you get the value for (y) . Like If i put in y=x+4, I get (y)=2. SO the solution will be (-2,2)
Reply if you have any further doubts, Read both the solutions again and again and you shall get it buddy

Answer 15

Sure, let me know if you don't follow any of these steps.
x+4=-2x-2
3x=-6
x=-2

Answer 16

@aadi4502 @thatonegirl_ You are amazing! Thank you soo much!!!

Answer 17

You are welcome! I hope that clears it up a bit?

Answer 18

And as @aadi4502 mentioned, you could also find/check your answer by graphing both lines and seeing where they intersect :)