How do solve y=-x+4 and y=x-6?

Answer 1

-x + 4 = x - 6
-4 -4

-x = x -10
-x -x

-2x = -10

divide both sides by -2

replace the x

x = 5
y = -1

Answer 2

Use substitution.

Substitute -x + 4from the first equation in place of y of the second equation.

-x + 4 = x - 6

add x to both sides

4 = 2x - 6

add 6 to both sides

10 = 2x

divide both sides by 2

5 = x

If x = 5 and y = -x + 4, then
y = -(5) + 4
y = -5 + 4
y = -1

Answer: (x, y) = (5, -1)

Answer 3

y=-x+4
y=x+6

first solve for y by cancelling out the x's

y+y=-x+x+4+6
2y=0x +10
2y=10
y=5

plug it into the original

(5)=x+6
-x=6-5
x=-1

answer x=-1 y=5
-1,5

Answer 4

Set the two equations equal to eachother:

-x + 4 = x - 6

10 = 2x

x = 5

Now, plug this back into one of the equation:

y = -(5) +4

y = -1

Answer 5

y= -x+4
&
y=x-6
+6.....+6

y+6=x

x=y+6

y= -(y+6)+4

y= -y -6+4 add y to each side

2y= -6+4

2y= -2 divide each side by a +2

y= -1

x=y+6

x= -1+6

x=5

ANSWERS: y= -1, x=5

Answer 6

Set them equal to each other:
-x + 4 = x - 6
4 = 2x - 6
2x = 10
x = 5

Answer 7

y=-x+4
y=x-6 subtract from the equation above
0=10 these are parallel lines. There is no solution.

Answer 8

- x + 4 = x - 6
10 = 2x
x = 5
y = - 1

Answer 9

y= -1 for both

Answer 10

y= -x+4.................................(1)
& y= x - 6...................................(2)

(2) - (1) => 2x - 10=0
=> 2x= 10
=> x = 5
(1)=> y = - 5 + 4
=> y = -1