Solve the following system of equations Enter your answers a

Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.)

6x + 3y = -12

25x 5y = 20

-19x + 8y = -32

Solution

We are given 6x+ 3y = -12 or, 2x + y = - 4 ...(1)

25x - 5y = 20 or, 5x - y = 4......(2)

-19x + 8y = -32...(3)

On addind the 1st and the 2nd equations, we get 2x + y + 5x - y = 4 + ( -4) or, 7x = 0 so that x = 0

Now, on substituting the value of x in the 1st equation, we get 0 + y = -4 or, y = - 4.

On substituting x = 0 and y = -4 in the 3rd equation, we get ( - 19 )(0) + 8 ( -4) = -32 or -32 = -32 which is correct. Thus the solution to the given system of equations is x = 0 and y = - 4. We can verify this result by substituting these values of x and y in the 2nd equation also.