Download Algebra I - MCPMathReadingFun9

Algebra I
Name:
Teacher:
Algebra 1, Period
CW 54A: Solving Systems by Elimination
(Day 2)
1) Consider the following system of equations: −3𝑦 + 4𝑥 = 25 and −3𝑥 + 8𝑦 = 10.

Can you solve this system using elimination without altering the equations?

What needs to be done in order to solve a system using elimination?

Now that my equations are in standard form, 4𝑥 − 3𝑦 = 25 𝑎𝑛𝑑 − 3𝑥 + 8𝑦 = 10, what common
coefficients can I find for the system?
4𝑥 − 3𝑦 = 25 
−3𝑥 + 8𝑦 = 10 
2) Identify the solution to the system of equations
by using elimination.
𝑦 − 7𝑥 = −19 𝑎𝑛𝑑 − 2𝑥 + 3𝑦 = −19
3) Identify the solution to the system of equations
by using elimination.
−3𝑥 + 7𝑦 = −16 𝑎𝑛𝑑 5𝑦 − 9𝑥 = 16
4) Find the intersection point of the graph of the
following linear equations:
8𝑥 + 14𝑦 = 4 𝑎𝑛𝑑 − 7𝑦 − 6𝑥 = −10
5) What ordered pair (x, y) will be true for both
equations?
4𝑦 + 5𝑥 = −30 𝑎𝑛𝑑 3𝑥 − 9𝑦 = −18
START STRONG. STAY HUNGRY. BE ONE.
Consider the following situation . . .
In Lewis Carroll’s Through the Looking Glass, Tweedledum says, “The sum of your weight and
twice mine is 361 pounds.” Tweedledee replies, “The sum of your weight and twice mine is 362
pounds.” Find both of their weights.
Can we solve this problem using only Tweedledum’s sentence?
If we have two unknown quantities, how many equations do we need to write in order to solve the
problem?
6) Generate a system of equations to represent the situation given. Then, solve the system.
Two groups of Muchin scholars and teachers went to a science museum. The museum charged the first
group of 28 scholars and 5 teachers $284 for the day and charged the second group of 40 scholars and 10
teachers $440 for the day. How much does the museum charge one student and one teacher?
Define your variables:
Can I use “s” and “t” as variables for my first equation and “x” and “y” as variables for my second
equation? Why or why not?
7) Generate a system of equations to represent the situation given. Then, solve the system.
One customer at Brianna’s Bagels and Bakery pays $5.67 for 3 bagels and 4 muffins. Another
customer pays $6.70 for 5 bagels and 3 muffins. How much does Brianna’s Bagels and Bakery charge
for one bagel and one muffin?
Define your variables:
START STRONG. STAY HUNGRY. BE ONE.
8) Generate a system of equations to represent the situation given. Then, solve the system.
Lulu tells her little brother, Jack, that she is holding 20 coins all of which are dimes and quarters. They
have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is
holding. Solve this problem for Jack.
Define your variables:
VANG it out . . .
Represent the solution to the following system using VANG!
Jon went to the store and purchased 5 snow shovels and 3 pairs of gloves and spent a total of $48.00. Kyle
went to the store and purchased 2 snow shovels and 6 pairs of gloves and spent a total of $32.00. How much
did one snow shovel and one pair of gloves cost?
Verbally (Explain what the solution means)
Algebraically (Solve the system using
elimination)
Numerically (Represent the system using a
table!)
Graphically (Graph the system!) Use a sheet of
graph paper!
START STRONG. STAY HUNGRY. BE ONE.
START STRONG. STAY HUNGRY. BE ONE.