Is 2x+3y=15 one solution

Answer 1

Hi, Elle! There's no way you can tell if it's one solution unless you graph it. First, however, we'll have to rewrite the equation as it's not in slope-intercept form then graph it.

The first step is to rewrite into slope-intercept form which is y = mx + b, and we'll do that by moving 2x to the other side to isolate y:

2x+3y=15

3y = -2x + 15 (we switched 2x's signs because we moved it from one side to another)

Alrighty! We have written it in slope-intercept form, but y isn't single as there's still 3 so we'll have to simplify by dividing 3 by each number:

3y = -2x + 15

3y/3 = 1/simply y

-2/3= - 2/3

+15/3 = +5

Now, that we've got our results, it's time to replace them with our current ones:

3y = -2x + 15

y = -2/3x + 5

Great! Now, we have our simplified equation, we'll graph it by creating a table of values (minimum is 2) :

y = -2/3x + 5

x │y

0 │ 3

1 │ 5

Let's plug it in!

y(3)= -2/3(0) + 5

3= -0+5 =5 which is (5,3)

y(5) = -2/3(1) + 5

5 = -2/3 + 5= 7/3 which is (7/3 , 5)

If you graph these points on a sheet of graph paper one or enter them in a graph calculator, you'll see this equation has infinite solutions, not one solution, so therefore, this equation doesn't have one solution but rather infinite solutions.