Question

The x-coordinate of the solution to:
2x-y=6
y=3x+4

The y-coordinate of the solution to:
y=-x+2
y=x+4

The y-coordinate of the solution to:
x=6
2x+y=3

The x-coordinate of the solution to:
y=4
2x-3y=2

The y-coordinate of the solution to:
y=6x-1
y=-2x+3

The y-coordinate of the solution to:
3x+y=9
6x-y=6

The x-coordinate of the solution to:
6x+2y=8
3x+2y=-7

The y-coordinate of the solution to:
x=0
y=6x-16

what is the sum of all of the answers to these equations

Answer 1

To find the solution for each system of equations, we'll solve them individually:

1) 2x - y = 6
y = 3x + 4

We can substitute the value of y from the second equation into the first equation:
2x - (3x + 4) = 6
2x - 3x - 4 = 6
-x - 4 = 6
-x = 10
x = -10

To find y, we substitute the value of x into the second equation:
y = 3(-10) + 4
y = -30 + 4
y = -26

So, the solution to this system is (-10, -26).

2) y = -x + 2
y = x + 4

Since both equations are in terms of y, we can set them equal to each other:
-x + 2 = x + 4
2x = 2
x = 1

To find y, we substitute the value of x into the first equation:
y = -(1) + 2
y = -1 + 2
y = 1

The solution to this system is (1, 1).

3) x = 6
2x + y = 3

We can substitute the value of x from the first equation into the second equation:
2(6) + y = 3
12 + y = 3
y = 3 - 12
y = -9

The solution to this system is (6, -9).

4) y = 4
2x - 3y = 2

We can substitute the value of y from the first equation into the second equation:
2x - 3(4) = 2
2x - 12 = 2
2x = 2 + 12
2x = 14
x = 7

The solution to this system is (7, 4).

5) y = 6x - 1
y = -2x + 3

Since both equations are in terms of y, we can set them equal to each other:
6x - 1 = -2x + 3
8x = 4
x = 4/8
x = 1/2

To find y, we substitute the value of x into the first equation:
y = 6(1/2) - 1
y = 3 - 1
y = 2

The solution to this system is (1/2, 2).

6) 3x + y = 9
6x - y = 6

We can add the two equations together to eliminate y:
(3x + y) + (6x - y) = 9 + 6
9x = 15
x = 15/9
x = 5/3

To find y, we substitute the value of x into the first equation:
3(5/3) + y = 9
5 + y = 9
y = 9 - 5
y = 4

The solution to this system is (5/3, 4).

7) 6x + 2y = 8
3x + 2y = -7

We can subtract the second equation from the first equation to eliminate y:
(6x + 2y) - (3x + 2y) = 8 - (-7)
3x = 15
x = 15/3
x = 5

To find y, we substitute the value of x into the first equation:
6(5) + 2y = 8
30 + 2y = 8
2y = 8 - 30
2y = -22
y = -22/2
y = -11

The solution to this system is (5, -11).

8) x = 0
y = 6x - 16

We substitute the value of x into the second equation to find y:
y = 6(0) - 16
y = -16

The solution to this system is (0, -16).

To find the sum of all the x-coordinates, we add the x-values from each solution:
-10 + 1 + 6 + 7 + 1/2 + 5/3 + 5 + 0 = -10 + 1 + 6 + 7 + 1/2 + 5/3 + 5 + 0 = 16 + 1/2 + 5/3 = 32/2 + 1/2 + 10/6 = 16 + 1/2 + 5/3 = 32/2 + 1/2 + 5/3 = 16 + 1/2 + 5/3 = 28/2 = 14.

To find the sum of all the y-coordinates, we add the y-values from each solution:
-26 + 1 + -9 + 4 + 2 + 4 + -11 + -16 = -26 + 1 + -9 + 4 + 2 + 4 + -11 + -16 = -51.

Therefore, the sum of all the answers to these equations is (-14, -51).

Answer 2

The x-coordinate of the solution to:
2x-y=6
y=3x+4

Answer 3

To find the x-coordinate of the solution, we can substitute the value of y from the second equation into the first equation:

2x - (3x + 4) = 6

Simplifying this equation will give us the value of x:

2x - 3x - 4 = 6

-x - 4 = 6

To isolate x, we can add 4 to both sides of the equation:

-x = 10

Multiplying both sides of the equation by -1, we get:

x = -10

Therefore, the x-coordinate of the solution is -10.