3x plus 6y equals 18 2x plus 5y equals 20?

Answer 1

You need to be more clear about your question.

3x + 6y = 18

2x + 5y = 20

The two equations you give represent lines. I assume you're trying to find the point at which they intersect. There are various ways to work this out.

One technique is to multiply each equation by a factor that gives one of the two variables the same coefficient. For example, if we multiply the first equation by 2, and the second equation by 3, we get:

6x + 12y = 36

6x + 15y = 60

Then we can subtract one from the other, which gives us a solution for y:

[6x + 12y = 36]

- [6x + 15y = 60]

_______________

[0x - 3y = -24]

So -3y = -24, telling us that at the point of intersection, y = 8. We can then plug that back into one of the original equations and solve for x:

2x + 5y = 20

2x + 5(8) = 20

2x = 20 - 40

2x = -20

x = -10

So the lines intersect at the point (-10, 8).

Another way to work it out is to solve one of the equations for a single variable, and then plug it into the other one:

3x + 6y = 18

∴ x + 2y = 6

∴ x = 6 - 2y

2x + 5y = 20

∴ 2(6 - 2y) + 5y = 20

∴ 12 - 4y + 5y = 20

∴ y = 20 - 12

∴ y = 8

That gives us the value 8 for y, which we can once again plug in to either of the original equations to find x:

2x + 5y = 20

∴ 2x + 40 = 20

∴ 2x = -20

∴ x = -10

Once again telling us that the lines intersect at the point (-10, 8)