Question

Given the system of linear equations.

x = y + 4
y = -2x - 4 Part A: Solve the linear system of equations by graphing Part B: Use substitution to solve the linear system of equations Part C: Use addition to solve the linear system of equations In your final answer, include all of your work, the graph of the equations and the solution.

Answer 1

a) See the graph below.
The solution is (x, y) = (0, -4).

b) Substituting for x, you have
.. y = -2(y+4) -4
.. y = -2y -12
.. 3y = -12
.. y = -4
.. x = y +4 = -4 +4 = 0
The solution is (x, y) = (0, -4).

c) Add the two equations.
.. (x) +(y) = (y +4) +(-2x -4)
.. x +y = y -2x . . . . . . . . . . . . eliminate parentheses
.. 3x = 0 . . . . . . . . . . . . . . . . add 2x -y
.. x = 0
.. y = -2x -4 = -2*0 -4 = -4
The solution is (x, y) = (0, -4).