LESSON1- SYSTEM OF LINEAR EQUATIONS

Solving systems of linear equations

By substitution

 
To solve using substitution, follow these four steps:
Step 1: Isolate a variable.
Step 2: Plug the result of Step 1 into the other equation and solve for one variable.
Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.
Step 4: State the solution.
 

By elimination

To solve using elimination, follow these four steps:

 


Step 1: Make sure the equations have opposite x terms or opposite y terms.
Step 2: Add to eliminate one variable and solve for the other.
Step 3: Plug the result of Step 2 into one of the original equations and solve.
Step 4: State the solution.
 
 

System of linear equations - Listening

Exercise 1.

At a community barbecue, Mrs. Patterson and Mr. Mullins are buying dinner for their families. Mrs. Patterson purchases 3 hot dog meals and 2 hamburger meals, paying a total of $36. Mr. Mullins buys 3 hot dog meals and 3 hamburger meals, spending $45 in all. How much do the meals cost?

 

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Exercise 1.

Nada owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 5 small tiers and 3 medium tiers, which will serve a total of 226 guests. The second one includes 5 small tiers and 5 medium tiers, which is enough servings for 310 guests. How many guests does each size of tier serve?

 

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System of equations - word problems

1) The owner of Stafford Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 3 small arrangements and 9 large arrangements, which took her a total of 75 minutes. After lunch, she arranged 14 small arrangements and 9 large arrangements, which took 86 minutes. How long does it take to assemble each type?

The florist can assemble a small arrangement in …………….minutes and a large one in …………..minutes.

 

2)A boutique in Richmond specializes in leather goods for men. Last month, the company sold 54 wallets and 57 belts, for a total of $6,171. This month, they sold 93 wallets and 57 belts, for a total of $8,199. How much does the boutique charge for each item?

The boutique charges $...............for a wallet, and $.............for a belt.

 

3)Hana is working furiously to knit scarves and beanies for a craft fair next weekend.

Yesterday she completed 2 scarves and 3 beanies, using a total of 22 meters of yarn.

The day before, she used 18 meters to knit 2 scarves and 2 beanies.

Assuming Hana is using the same pattern and type of yarn for each scarf and beanie,

how much yarn does each project require?

Each scarf requires …………meters of yarn, and each beanie requires ………meters.

 

 

See more - Materials !

Materials

System_equations_listening.pdf
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System_equation_Tasks.pdf
Adobe Acrobat Document 65.6 KB