Semester Review - Systems of Linear Equations & Inequalities

Semester Review

Systems of Linear Equations & Inequalities

Methods for solving systems of equations

1. Substitution

2. Graphing

3. Elimination

4. Matrix

1. Substitution

Step 1: rearrange one equation to solve for the variable of your choice

Step 2: substitute into the other equation, find value for that variable

Step 3: substitute value back into first equation, find value for second variable

Step 4: repeat as necessary

Multiple Choice

What is the solution for the following system?

 $-2x+y=1$  

 $3x+y=-4$  

•  $x=-1$  ,  $y=-1$  

•  $x=1$  ,  $y=1$  

•  $x=-1$  ,  $y=1$  

•  $x=1$  ,  $y=-1$  

Remember: Solutions to the system can also be written in (x, y) format

This the intersecting point of the system's graph

Multiple Choice

For the system we just solved, what is the solution in (x, y) format?

 $-2x+y=1$  

 $3x+y=-4$  

• (-1, 1)

• (1, 1)

• (-1, 1)

• (1, -1) 

1. Substitution (continued)

For solving 3x3 systems of equations...

Use the cascade approach:

solve the shortest/simplest equation first, then work your way up to the longest/hardest equation last.

Multiple Choice

What is the solution to the following 3x3 system?

hint:  answer is given in (x, y, z) format

 $x+3y+z=-3$  

 $x+y=-2$ 
 $4x-2y=16$    

• (6, 4, -21)

• (2, -4, 7)

• (6, -8, 15)

• (2, -4, -13)