Question

solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. if the system has one solution, find the solution. -3x+ y=20, x+y=-4

Answer 1

one solution (- 6, 2 )

Explanation:

- 3x + y = 20 → (1)

x + y = 4 ( subtract x from both sides )

y = - x - 4 → (2)

substitute y = - x - 4 into (1)

- 3x - x - 4 = 20

- 4x - 4 = 20 ( add 4 to both sides )

- 4x = 24 ( divide both sides by - 4 )

x = - 6

substitute x = - 6 into (2)

y = - x - 4 = - (- 6) - 4 = 6 - 4 = 2

solution is (- 6, 2 )