3x+6y=21

-5x+2y=13

2 answers

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the elimination method in this case:

First, let's multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same:

6x + 12y = 42
-15x + 6y = 39

Next, we add the two equations together to eliminate y:

6x + 12y - 15x + 6y = 42 + 39
-9x + 18y = 81

Now, we can simplify this equation:

-9x + 18y = 81
-9x = 81 - 18y
x = (81 - 18y)/-9
x = -9 + 2y

Now, we can substitute this expression for x back into one of the original equations. Let's use the first equation:

3(-9 + 2y) + 6y = 21
-27 + 6y + 6y = 21
12y = 48
y = 4

Now that we have found the value of y, we can substitute it back into the expression for x:

x = -9 + 2(4)
x = -9 + 8
x = -1

Therefore, the solution to the system of equations 3x + 6y = 21 and -5x + 2y = 13 is x = -1 and y = 4.

-3x-4y=-23
3x-5y=5