please tell me the answer to this algebraic problem?

Question

what is the point of intersection between these two equations on a four quadrant graph: y=6-x
y=3x-10
thanks

heres another one... please help, im just learning and my teachers suck.
the slope and y-intercept of 9x-3y=81

Answer 1

Set your two equations equal to each other and solve for x:

6-x = 3x-10
16 = 4x
4 = x
Substituting back into either equation makes y = 2

so the point of intersection is (4,2)

Answer 2

Y=5

Answer 3

This is a system of two equations in two unknowns. Solving the system gives you the point of intersection.

1) y = 6 - x
2) y = 3x - 10

Equation 1 is solved for y in terms of x - use this result by substituting for y in equation 2

6 - x = 3x - 10
- 4x = - 16 {subtract 3x and 6}
x = 4 {divide by -4}

Put this result into equation 1

y = 6 - 4
y = 2

Check in equation 2

2 = 3(4) - 10
2 = 12 - 10
2 = 2

The lines intersect at (4, 2)

Answer 4

Because the graphs are intersecting at the same point, their x and y values will be the same.

Both equations are already in slope-intercept form, so we can set them equal to each other...

6-x = 3x - 10
4x = 16
x = 4

Plug 4 in either equation to find the y value.
y = 6-4
y = 2

Therefore, the two lines will intersect at the point (4,2).

Hope that helped.

Answer 5

First, you have to set both equations into y=mx+b format. After you do that, graph them! Voila! Immediate intersection answer!

Answer 6

this is using a system of equations
first subsitute
6-x=3x-10
16=4x
4=x
plug the x value into either equation
y=6-(4)
y=2
therefore the pt is (4,2)