1. 31
Today:
Warm-Up: (4)
Review Systems of Equations
New Solving Techniques
Monday: Review for Test Tuesday
4th Period: Only 10 Notebooks submitted
Please leave notebooks again before you
leave.
2. Warm the
a. Write the equation ofUp line
b. Write the inequality an the line. for a line
1. Write of equation
perpendicular to 2x -4y = -2
2. Solve for a: 9a – 2b = c + 4a
3. 4. Write the systems of equations
shown by the graph below.
4. Review: Solve Systems of Equations by Graphing
1 =
1+0
2 +
( + 0)
1 = 3
(2,1)
Step 1: Put both equations in
slope - intercept form.
Step 2: Graph both equations on
the same coordinate plane.
Step 3: Plot the point where the
graphs intersect.
Step 4: Check to make sure your
solution makes both equations true.
5. Review: Solve Systems of Equations by Elimination
(addition or subtraction)
Elimination is easiest when the equations
are in standard form.
1: Put the equations in
Standard Form.
Step 2: Determine which
variable to eliminate.
Step 3: Add or subtract
the equations.
Step 4: Plug back in to
find the other variable.
Step 5: Check your
solution.
Standard Form: Ax + By = C
Look for variables that have
the same coefficient.
Solve for the variable.
Substitute the value of the
variable into the equation.
Substitute your ordered pair
into BOTH equations.
6. Review: Solve Systems of Equations by Elimination
(addition or subtraction)
2x + 7y = 31
5x - 7y = - 45
7x + 0 = -14
x = -2
Like variables must be lined under each other.
THEN----
7. Review: Solve Systems of Equations by Elimination
(addition or subtraction)
2X + 7Y = 31
2(-2) + 7y = 31
-4 + 7y = 31
Substitute your
4
4
answer into either
original equation
and solve for the
second variable.
7y = 35; y = 5
Solution
(-2, 5)
Now check our answers in both
equations------
9. Solve Systems of Equations by Elimination
(Multiplying)
Like variables
must be lined
under each
other.
x + +y1y 4 4
1x = =
2x + 3y = 9
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.
10. Solve Systems of Equations by Elimination
(Multiplying)
( X + Y = 4) -2
2X + 3Y = 9
-2X - 2 Y = - 8
2X + 3Y = 9
Now add the two
equations and solve.
THEN----
Y=1
11. Solve Systems of Equations by Elimination
(Multiplying)
X+Y=4
X +1=4
- 1 -1
X=3
Solution
Substitute your
answer into either
original equation
and solve for the
second variable.
(3,1)
Now check our answers in both equations--
13. Solve Systems of Equations by Elimination
(Multiplying)
3x – 2y = -7
2x -5y = 10
Can you multiply either equation
by an integer in order to eliminate
one of the variables?
Here, we must multiply both
equations by a (different)
number in order to easily
eliminate one of the variables.
Eliminate
Plug back in
Solve for other
variable
Multiply the top
equation by 2, and the
bottom equation by -3
Write your solution as
an ordered pair
(-5,-4)
Plug both solutions into
original equations
15. 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
value of x ?
-4
At this point we substitute -4 for
x, and solve for y. This is exactly
what the substitution method is
except it is done at the beginning.
16. Solve: By Substitution
Example 1: y = 2x
4x - y = -4
Since the first equation tells us
that y = 2x, replace the y with 2x
in the second equation.
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
