-x - y = 1 y = x + 3 If the two equations are graphedat what point do the lines representing the two equations intersect A(-1, 2) B(-2, 1) C(1, -2) D(2, -1) ?

Question

I've tried doing these, but no matter what I get them wrong

Answer 1

T the point of intersection, the 2 line are equal to each other.

 

Therefore:

 

 

Substitute y=x+3 into the other equation of -x-y=1

 

that yields -x-(x+3) = 1

 

This yields -x-x-3=1: Solve for x

 

-2X-3=1

-2x=1+3=4

-2X=4;  therefore divide both sides by -2

X = -2

 

Substitute the X value of -2 back into 1 of the original equations and solve for  YY=X+3

Y=(-2)+3

Y = 1          YOUR ANSWER IS:  B(-2,1)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Answer 2

The problem asks, "If the two lines are graphed ...," so let's try that method to answer the problem.  Note: to find the y value for each point, plug the x value into the equation and plot the points.

 

The line  -x -y = 1 can be written as  y = -x-1  and contains the points:

    (-2,1)

    (-1.0)

    (0,-1)

    (1,-2)

    (2,-3)

 

The line  y = x+3  contains the points:

   (-2,1)

   (-1,2)

   (0,3)

   (1,4)

   (2,5)

 

The point that is in both lists and is on both lines is (-2,1).

Answer 3

Jessica, another way to solve this is to plug in each point and see which makes BOTH equations true.

 

-x - y = 1

-(-1)  - 2 = 1

1 - 2 = 1

-1 = 1

Already not true, so this one is out.

 

Again, find the point that makes both equations true.

 

Answer 4

From what I understand, the questions is asking at what point do the two lines representing by the equations: -x - y = 1 and y = x + 3 intersect. I'm guessing that the four points listed are multiple choice options. If so, our answer must be one of them as the two lines will intersect at only one point. 

 

At the point where the two lines intersect the dependent variable Y of one equation will equal the other, 

 

Y = X + 3

-X - Y = 1 -> Y = -(X + 1)

 

X + 3 = -(X + 1) -> X + 3 = -X - 1 -> 2X + 3 = -1 -> 2X = -4 -> X = -2.

 

Plug -2 back into the equations.

 

Y = -2 + 3 = 1.

Y = -(-2 + 1) = -(-1) = 1.

 

Confirming that X and Y are the same, this is the intersection point.

 

Therefore, the answer is B) (-2,1).