3x+6y=21

Question

–5x+2y=13

Answer 1

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

Step 1: Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations equal:

15x + 30y = 105 (5 * (3x + 6y = 21))
-15x + 6y = 39 (-5 * (-5x + 2y = 13))

Step 2: Add the two equations to eliminate x:

15x + 30y - 15x + 6y = 105 + 39
36y = 144
y = 4

Step 3: Substitute y = 4 into the first equation to solve for x:

3x + 6(4) = 21
3x + 24 = 21
3x = -3
x = -1

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