# 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.

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:**

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**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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**http://www.voki.com/pickup.php?scid=7004922&height=400&width=300**

**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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**http://www.voki.com/pickup.php?scid=7315465&height=267&width=200**

## 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.**

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**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.**

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**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.**

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**See more - Materials !**