Activity
Solve each system of equations without graphing, show your reasoning,
and check your solutions.
System A
Use System A to answer questions 1 – 3.
1.
What is the value of ?
2.
What is the value of ?
3.
Show your reasoning and check the solution.
Compare your answer:
System B
Use System B to answer questions 4 – 6.
4.
What is the value of ?
5.
What is the value of ?
6.
Show your reasoning and check the solution.
Compare your answer:
System C
Use System C to answer questions 7 – 9.
7.
What is the value of ?
8.
What is the value of ?
9.
Show your reasoning and check the solution.
Compare your answer:
System D
Use System D to answer questions 10 – 12.
10.
What is the value of ?
11.
What is the value of ?
12.
Show your reasoning and check the solution.
Compare your answer:
Are you ready for more?
Extending Your Thinking
This system has three equations:
1.
Add the first two equations to get a new equation.
Compare your answer:
2.
Add the second two equations to get a new equation.
Compare your answer:
Solve the system of your two new equations, then answer questions
3 and 4.
3.
What is the value of ?
4.
What is the value of ?
Solve the original system of equations, then answer questions 5 – 7.
5.
What is the value of ?
6.
What is the value of ?
7.
What is the value of ?
A mechanic’s garage purchased 8 brake pads and 5 headlight sets for inventory and paid $1,460. Later, the mechanic purchased another order of 6 of the same brake pads and 5 of the same headlight sets and paid $1,220. How much does each part cost?
-
brake pads: $80; headlight sets: $148
-
brake pads: $80; headlight sets: $140
-
brake pads: $100; headlight sets: $100
-
brake pads: $120; headlight sets: $100
Additonal Resources
Solving a System of Equations by Elimination
Let’s reinforce the steps to solve a system of equations using
elimination.
Step 1 - Write both equations in standard
form. If any coefficients are fractions, clear them.
Step
2 - Check to see if the coefficients of one variable are opposites or
equivalent.
Step 3 - Add or subtract the
equations to eliminate one variable.
Step 4
- Solve for the remaining variable.
Step 5
- Substitute the solution from Step 4 into one of the original equations. Then solve for
the other variable.
Step 6 - Write the
solution as an ordered pair.
Step 7 -
Check that the ordered pair is a solution to both original equations.
Example
Let’s look at an example. Solve the following system of equations
using elimination:
Step 1 - Write both equations in standard form.
If any coefficients are fractions, clear them.
Step 2 - Check to see if the coefficients of one
variable are opposites or equivalent. The coefficients on the -variables are opposites. We can
add the equations.
Step 3 - Add the equations to eliminate one
variable.
Step 4 - Solve for the remaining variable.
Step 5 - Substitute the solution from Step 4 into
one of the original equations. Then solve for the other variable.
\begin{array}{rcl}3x-3y&=&-24\\3x-3(3)&=&-24\\3x-9&=&-24\\3x&=&-15\\x&=&-5\end{array}
Step 6 - Write the solution as an ordered pair.
Step 7 - Check that the ordered pair is a
solution to both original equations.
Solving a System of Equations by Elimination
Solve the following system of equations using elimination:
Compare your answer:
Here is how to solve this system of equations using
elimination:
Step 1 - Write both equations in standard
form. If any coefficients are fractions, clear them.
Step 2 - Check to see if the coefficients
of one variable are opposites or equivalent. The coefficients on the -variables
are opposites. We can add the equations.
Step 3 - Add the equations to eliminate
one variable.
Step 4 - Solve for the remaining
variable.
Step 5 - Substitute the solution from
Step 4 into one of the original equations. Then solve for the other variable.
Step 6 - Write the solution as an ordered
pair.
Step 7 - Check that the ordered pair is a
solution to both original equations.