What are the coordinates of the point of intersection?

Question

Hi, I have a Algebra Eoc practice due tomorrow and I am really confuzed about this question. It will be really helpful if you can tell me the steps, thanks!

2X-4Y=6

3X+Y=-5

A. (-1,-8)  B.(-3,-3)  C.(-1,-1)  D.(1,-1)  E.(-1,-2)

Answer 1

 

2x-4y=6

3x+y=-5

by elimination...

multiply the second equation by 4

12x+4y=-20

2x-4y=6

add

14x+0=-14

14x=-14

x=-1

substitute

2(-1)-4y=6

-2-4y=6

-4y=6+2

-4y=8

y=8/-4

y=-2

(-1,-2) which is E)

by substitution...

2x-4y=6

3x+y=-5

y=-3x-5

substitute

2x-4(-3x-5)=6

2x+12x+20=6

14x+20=6

14x=6-20

14x=-14

x=-1 again

now substitute as above to get y=-2

(-1,-2) again

Answer 2

2x-4y=6

3x+y=-5

 

Both of the above equations are straight lines.  If they are not parallel (or the same line), they will cross (intersect) at one point; and at that point, the two lines are equal

 

Let's multiply the second equation by 4 so we can eliminate the y-variable when we add the two equations:

 

4*(3x + y = -5)

12x + 4y = -20

 

Now add the first equation and the modified second equation:

 

     2x  -  4y =    6

+ 12x + 4y = -20

------------------------

    14x  + 0  = -14

 

-14x = 14

x = -1

 

To solve for y, substitute x = -1 into either original equation and solve for y:

 

3x + y = -4

3(-1) + y = -5

-3 + y = -5

y = -2

 

The answer is E. (-1,-2)

 

 

Answer 3

2x-4y=6

3x+y=-5

 

y=-5-3x

 

2x-4(-5-3x)=6

2x+20+12x=6

14x=-14

x=-1

 

y=-5-3(-1)

y=-2

 

The resulting coordinates for the point of intersection is .....

 

(-1,-2)