The document provides examples for solving systems of equations through various methods like elimination, substitution, and word problems. It demonstrates setting up systems as equations based on information provided, choosing an elimination method by adding or multiplying equations, isolating variables, substituting values, and checking solutions. Word problems are converted to systems of equations and then solved to find unknown variable values.

1. Today:
 This Week's Khan Academy
 Systems of Equations
 4th & 5th Periods: Leave Notebooks
 Final Exam Scores
March 29, 2016

2. Warm Up
1. Write an equation for a line
perpendicular to 2x -4y = -2
2. Solve for a: 9a – 2b = c + 4a
a. Write the equation of the line
b. Write the inequality of the graph.

3. 4. Write the systems of equations
shown by the graph below.

10. Is it independent or dependent?
Is it consistent or inconsistent?
Is it independent or dependent?
Is it consistent or inconsistent?

11. Determine whether the ordered pair is
a solution of the given system.
The ordered pair (5, 2) makes both equations true.
(5, 2) is the solution of the system.
Substitute 5 for x and 2 for y in
each equation in the system.
2 – 2 0
0 0
0 3(5) – 2 13
15 – 2 13
13 13
3x – y 13
(5, 2);
3x – y = 13
𝟐
𝟓
x – y = 0
𝟐
𝟓
x – y = 0

12. –2 + 3(2) 4
x + 3y = 4
–2 + 6 4
4 4
–x + y = 2
– (–2) + 2 2
4 2
(–2, 2) is not a solution
of the system.
If an ordered pair does not satisfy the first equation in the
system, there is no reason to check the other equation(s).
Helpful Hint
Determine whether the ordered pair is
a solution of the given system.

13. SOLVING SYSTEMS BY ELIMINATION:
1. Arrange the like variables in columns.
2. Pick a variable, x or y, and make the two
equations opposites using multiplication.
3. Add the equations together (eliminating a
variable) and solve for the remaining variable.
4. Substitute the answer into one of the
ORIGINAL equations and solve.
5. Check your solution.
(BY ADDITION OR SUBTRACTION)

14. 5x - 4y = -21
-2x + 4y = 18
We need to eliminate (get rid of) a variable by cancelling out
one of the variables. We then solve for the other variable.
3x + 0 = -3
x = -1
THEN----
Like variables must be lined under each other.
What should we eliminate first?
Solve: By Elimination
Do we add or subtract the two equations?

15. 5x - 4y = -21
(-1, 4)
Substitute your first
solution into either original
equation and solve for the
second variable.
The solution to this system
of equations is:
Now check your answers in
both equations------
5(-1) – 4y = -21
-5 – 4y = -21
5 5
-4y = -16 y = 4

16. 5x + 4y = -21
-2x + 4y = 18
Solve: By Elimination
This system is nearly identical to the
previous example with one difference.
How must we proceed?

17. We actually have four options; what are they?
3x + y = 29
x + 4y = 6
We need to eliminate (get rid of) a variable. To simply
add this time will not eliminate a variable.
SOLVING SYSTEMS BY ELIMINATION:
(BY MULTIPLICATION)
1. Multiply the first equation by 4
2. Multiply the second equation by 3
3. If you want to add, then Multiply the first equation by...
4. If you want to add, then Multiply the second equation by...

18. 3x + y = 29
x + 4y = 6( ) - 3x + 12y = 18
Now subtract the two
equations and solve.
-11y = 11
- 11 - 11
y = - 1
THEN----
3x + y = 29
Substitute your answer into either
original equation and solve for the
second variable.

19. 2x - 5y = 2
-3x + 2y = -14

21. Which of the two equations would be
the easiest for isolating a variable?
SOLVING SYSTEMS BY SUBSTITUTION:

22. SOLVING SYSTEMS BY SUBSTITUTION:
1. Isolate (solve) one of the equations for x or y.
2. Substitute your new expression from Step 1 into
the other equation and solve for the variable.
3. Plug that solved variable into the other equation
from Step 1 and solve for the other variable.
4. Check your answers by plugging it into the
original equations.
- Get x or y by itself.

23. SOLVING SYSTEMS BY SUBSTITUTION:

25. Use ‘g’ for gloves and ‘h’ for hats.
Equation 1: 2g + 4h = $42.00
Equation 2: 2g + 2h = $30.00
0g + 2h = $12.00
Hats are $6.00 each
2g + 24 = $42.00
Plug both values in
and check for
equality.

26. SOLVING SYSTEMS WORD PROBLEMS:
Kelly went back-to-school shopping this weekend. She
spent $160 on jeans and shirts. She bought a total of
12 items, with jeans costing $16 and shirts costing $12.
How many jeans and shirts did she buy?
1. Mark
the text.
2. Label
variables.
j = jeans
s = shirts
3. Create
equations.
16j + 12s = 160
What’s the 2nd equation?j + s = 12
4. Solve.
5. Check.

27. Mrs. Smith took her family and friends to
the movies. There were a total of 12 people.
Children tickets cost $5 and adult tickets cost
$10. She spent a total of $95. How many adults
& how many children went to the movies?
1. Mark
the text.
2. Label
variables.
3. Create
equations.
4. Solve.
5. Check.