Question

(2x-y=-10) and (1/2x-1/3y=1). Solve the equations.

a) (x = -6, y = -2)
b) (x = 4, y = 6)
c) (x = -2, y = -6)
d) (x = 6, y = 4)

Answer 1

To solve the system of equations (2x-y=-10) and (1/2x-1/3y=1), we apply the elimination method, which leads to the solution (x=26, y=62).

Step-by-step explanation:

To solve the system of equations (2x-y=-10) and (1/2x-1/3y=1), we will use the substitution or elimination method. Let's align the equations properly for the elimination method:

1. Multiply the second equation by 6 to eliminate fractions: (3x-2y=6).
2. Now we have a new system of equations: (2x-y=-10) and (3x-2y=6).
3. To eliminate y, multiply the first equation by 2 and subtract from the second equation: (2x-y)*2 => (4x-2y=-20) and then (3x-2y) minus (4x-2y) gives us (-x=-26), so x=26.
4. Substitute x=26 back into the first equation (2x-y=-10) to find y: (2*26-y=-10) gives y=52+10 => y=62.

Therefore, the solution to the system of equations is (x=26, y=62).