Question

How do you solve y=−2x−9 and y=x+9 together, written out in the right order and step by step?

a. Elimination method: Combine the equations and solve for x and y.
b. Substitution method: Substitute the expression for y from one equation into the other and solve for x and y.
c. Graphical method: Plot the two equations on a graph and find the intersection point.
d. Not mentioned

Answer 1

To solve the system of equations, you can use the elimination method, substitution method, or graphical method.

Step-by-step explanation:

The given system of equations is:

y = -2x - 9

y = x + 9

1. Elimination method: Add the two equations together to eliminate the variable y:
   -2x - 9 + x + 9 = 0
   -x = 0
   x = 0
   Substitute the value of x into one of the original equations:
   y = 0 + 9
   y = 9
2. Substitution method: Solve one equation for y in terms of x:
   y = x + 9
   Substitute this expression for y into the other equation:
   -2x - 9 = x + 9
   -3x = 18
   x = -6
   Substitute the value of x into one of the original equations:
   y = -6 + 9
   y = 3
3. Graphical method: Plot the two equations on a graph and find their intersection point.
   The intersection point is (0, 9). This represents the values of x and y that satisfy both equations.