1. 3.2 Solve Linear Systems Algebraically

2. The Substitution Method
x = -2y + 2
Solve this equation for x
Substitute -2y + 2 for x in the first equation.
3x + 4y = -4
3(-2y+2)+4y = -4
-6y+6+4y = -4
Finally, substitute 5 for y (in x = -2y +2) and solve for x.
x = -8
y = 5
(-8,5) is the solution to the system.

3. The Substitution Method
Check the ordered pair (-8,5) by substituting it into each equation to verify it is really the solution.
x = -8
y = 5
(-8,5) is the solution to the system.

4. The Linear Combination Method: Multiplying One Equation
Multiply the first equation by -2 -2
Add the equations together
3y = -18
y = -6
Use this value for y and substitute it into either of the equations. Solve for x.
The ordered pair (-11/2,-6) is the solution to this system
x=-(11/2)
4x – 5(-6) = 8

5. The Linear Combination Method: Multiplying One Equation
Multiply the first equation by -2 -2
3y = -18
Why Choose the multiplier -2??
y = -6
The ordered pair (-11/2,-6) is the solution to this system
x=-(11/2)

6. (1/2,4)

7. Solve the system using the Linear Combination Method.
(-1,5)

8. What about these??
a. x-2y=3 b. 6x-10y=12
2x-4y= x+25y=-30