x-y=10 and 5x-y=-6 what is x and y?

Question

x-y=10
5x-y=-6
what is x and y?

Answer 1

Elimination method :

The system of equations are

x - y = 10     → (1)

5x - y = - 6   → (2)

Since the coefficient of the y - term in two equations is same, i can eliminate these terms by subtracting the equations.

Write the equations in column form and subtract to eliminate variable y.

      x - y = 10

( - )5x - y = - 6

   ______________

- 4x = 16

The resultant equation is - 4x = 16 and solve it for x.

Divide each side by negative 4.

- 4/- 4 x = 16/- 4

Cancel common terms.

x = - 4.

Substitute the value of x = - 4 in equation 2: 5x - y = - 6 and solve for y.

5(- 4) - y = - 6

- 20 - y = - 6

Add 20 to each side.

- y = 14

Divide each side by negative 1.

y = - 14.

The solution is (- 4, - 14).