Question

How to find intersection from -8x+3y=11 and y=3x+4

Answer 1

Answer:

(-1,1)

Step-by-step explanation:

To find where both lines intersect, solve for x and y with substitution.

Equation 1.

-8x+3y=11

Equation 2.

y=3x+4

Substitute y from equation 2 into equation 1.

-8x+3(3x+4)=11

-8x+9x+12=11

x=-1

Now plug x into the second equation to solve for y.

y=3(-1)+4

y=-3+4

y=1

Both lines intersect at (-1,1)

Answer 2

Answer:

  (-1, 1)

Step-by-step explanation:

It's somewhat difficult to find the point of intersection when graphing these by hand, but a graphing calculator can show it easily.

The lines intersect at (-1, 1).

__

You are given an expression for y, which makes it easy to use substitution as a solution method. Using the second equation to substitute for y in the first equation, we get ...

  -8x +3(3x +4) = 11

  x +12 = 11 . . . . simplify

  x = -1 . . . . . . . subtract 12

Substituting back into the second equation, we find y to be ...

  y = 3(-1) +4 = 1

The lines intersect at (x, y) = (-1, 1).

_____

Additional comment

The slopes are 8/3 and 3. When hand-drawn lines have nearly the same slope, it is difficult to tell exactly where they intersect. Of course, a graphing calculator does not have the problem of finite line width and an apparent long region of intersection. It can pinpoint the intersection exactly.

Of course, "substitution" is not the only way this system of equations can be solved. However, for this system, it is one of the easiest when doing the solution by hand.