Question

solve the system of equations.
3x + 6y = 21
-5x + 2y = 13
(_,_)

Answer 1

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

First, we'll multiply the second equation by 3 to match the coefficients of x when we add the two equations together:

3*( -5x + 2y ) = 3*13
-15x + 6y = 39

Now, we will add this modified equation to the first equation:

3x + 6y - 15x + 6y = 21 + 39
-12x + 12y = 60
Divide through by -12:
x - y = -5
x = y - 5

Now we can substitute x back into the first original equation to solve for y:

3(y - 5) + 6y = 21
3y - 15 + 6y = 21
9y - 15 = 21
9y = 36
y = 4

Now we can substitute y back into x = y - 5 to solve for x:

x = 4 - 5
x = -1

Therefore, the solution to the system of equations is x = -1 and y = 4.