Question

Write two solutions for the following equation 2x+3y=24.

Answer 1

Answer: (12, 0) and (0, 8)

Explanation:

This equation is in standard form. We can sub in a number for x to solve for y and vice versa.

Let's sub in 0 for x.

`2x+3y=24\\2(0)+3y=24\\3y=24\\(3y)/(3) =(24)/(3) \\y=8`

When x is 0 y is 8 giving us the coordinate (0, 8).

Now lets sub in 0 for y

`2x+3(0)=24\\2x=24\\(2x)/(2) =(24)/(2) \\x=12`

When y is 0 x is 12 giving us the coordinate (12, 0)

Answer 2

Explanation:

Begin by solving for y

3y = -2x + 24 divide by 3

y =-(2/3)x + 24

Choose x so that it is divisible by 3

Let x = 6 which 3 can divide into evenly

y = -(2/3)*6 + 24 3 into 6 is 2 so you are left with

y = - 2 * 2 + 24

y = - 4 +24

y = 20

By a similar mthed, let x = 15

y = -2/3 x + 24

y = -2/3 * 15 +24

y = -2 * 5 + 24

y = -10 + 24

y = 14

So your two solutions are

(6,20)

(15,14)