Steps are shown for solving systems of equations by the elimination method, including multiplying one equation by a constant to eliminate a variable before adding the equations. Examples are provided of solving systems by substitution, where one variable is solved for in one equation and substituted into the other equation. Practice problems are given for students to apply

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Today:
Warm-Up
Review Systems of Equations
New Solving Techniques

2. Warm Up
1.

3. Warm Up
2. Solve for a: 9a – 2b = c + 4a 3. Solve by graphing and
state the solution
4. a. Write the equation of the line
b. Write the inequality of the line.

4. Warm Up
5. If it takes eight carpenters (all working at the same
time and rate) fifteen days to build a house, how long
will it take for ten carpenters to build the same house?
8 carpenters • 15 days = 120 carpenter-days.
Therefore 10x (x being the number of days)= 120.
x = 12 days for 10 carpenters
5. 1/3(3/5x + 18) = 3/4x +2/5

5. Review: Solve by Elimination
Practice 1: y = x + 7
x + 2y = 5
Practice 2: x - 3y = 7
3x +3y = 9

6. Solve: Elimination By Multiplying
0x + y = = 4
x + 0y 4
Like variables
must be lined 2x + 3y = 9
under each other.
We need to eliminate (get rid of) a variable.
To simply add this time will not eliminate a variable. If there was
a –2x in the 1st equation, the x’s would be eliminated when we
add. So we will multiply the 1st equation by a – 2.

7. Solve: Elimination By Multiplying
( X + Y = 4 ) -2 -2X - 2 Y = - 8
2X + 3Y = 9 2X + 3Y = 9
Now add the two equations Y=1
and solve.
THEN----

8. Substitute your answer into either original equation and
solve for the second variable.
X+Y=4
X +1=4
- 1 -1
X=3
Answer (3,1)
Now check our answers in both equations--

9. Solve: Elimination By Multiplying
x+y=4
3+1=4
4=4
2x + 3y = 9
2(3) + 3(1) = 9
6+3=9
9=9

10. Solve: By Substitution
Recall that when we 'solve' a point-slope formula, we
end up in slope-intercept form. In much the same
way, the substitution method is closely related to the
elimination method.
After eliminating one variable and solving for the other, we
substitute the value of the variable back into the equation.
For example: Solve 2x + 3y = -26 using elimination
4x - 3y = 2
What is the At this point we substitute -4 for x,
value of x ? and solve for y. This is exactly
what the substitution method is
except it is done at the beginning.

11. Solve: By Substitution
Example 1: y = 2x
4x - y = -
4
Example 1: Substitute 2x for y in the 2nd equation
y = 2x
4x - 2x = -4; 2x = -4; x = -2
Then, substitute -2 for x in the first equation:
y = 2(-2); y = -4
Finally, plug both values in and check for equality.
-4 = 2(-2); True; 4(-2) - (-4) = -4; -8 + 4 = -4; True

12. Solve: By Substitution
Example 2: 3x + 5y = -7
x = 2y + 5
Example 3: y = 2x - 1
6x - 3y = 7

13. Applying Systems of Equations
Solve by Elimination.
Example 1: The sum of two numbers is 52.
The larger number is 2 more than 4 times
the smaller number. Find both numbers.
Example 1: -(x + y = -52
-x - y = 52)
x+y=
52 + _________ Rearrange
x = 4y + 2
-4y = 2
-5y = -50 y = 10
x + 10 = 52; x = 42

14. Class Work: