3x+6y=21

Question

–5x+2y=13

Answer 1

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

Let's use the elimination method to solve for x and y:

First, multiply the second equation by 3 to make the coefficients of x in both equations the same:

-15x + 6y = 39

Now, add the two equations together:

(3x + 6y) + (-15x + 6y) = 21 + 39
-12x + 12y = 60

Divide the entire equation by 12 to simplify:

- x + y = 5

Now, we have a new equation:

x + y = 5 --> y = 5 - x

Now substitute this value of y into the first equation:

3x + 6(5 - x) = 21
3x + 30 - 6x = 21
-3x + 30 = 21
-3x = -9
x = 3

Now, substitute the value of x back into the equation y = 5 - x:

y = 5 - 3
y = 2

Therefore, the solution to the system of equations is x = 3 and y = 2.