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**Solving a system of equations by SUBSTITUTION**

Step 1: Solve an equation for one variable. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Step 2: Substitute Put the equation solved in Step 1 into the other equation. Step 3: Solve the equation. Get the variable by itself. Step 4: Plug back in to find the other variable. Substitute the value of the variable into the equation. Step 5: Check your solution. Substitute your ordered pair into BOTH equations.

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**1) Solve the system using substitution**

x + y = 5 y = 3 + x Step 1: Solve an equation for one variable. The second equation is already solved for y! Step 2: Substitute x + y = 5 x + (3 + x) = 5 2x + 3 = 5 2x = 2 x = 1 Step 3: Solve the equation.

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**1) Solve the system using substitution**

x + y = 5 y = 3 + x x + y = 5 (1) + y = 5 y = 4 Step 4: Plug back in to find the other variable. (1, 4) (1) + (4) = 5 (4) = 3 + (1) Step 5: Check your solution. The solution is (1, 4). What do you think the answer would be if you graphed the two equations?

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**Solve the system using substitution**

3x – y = 4 x = 4y - 17

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**Solving a system of equations by SUBSTITUTION**

Pick the easier equation. The goal is to get y= ; x= ; a Step 1: Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. . Put the equation solved in Step 1 into the other equation Using the equation solved in Step 1 replace the variable in the other equation. Therefore you have one equation with one variable. Step 2: he variable by itself. ck the easier equation. The goal is to get y= ; x= ; a= ; etc Step 3: Get the variable by itself. . Substitute the value of the variable into the equation. Write your answer as an ordered pair (x, y). Step 4:

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REAL WORLD APP You buy a total of 50 burgers and hotdogs for $90. You pay $2 per burger and $1.50 per hotdog. Write a system of equations to find the number of x burgers and y hotdogs.

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**Solve the system by substitution**

_______burgers and ______hotdogs

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Try this: You sell lemonade for $2 per cup and orange juice for $3 per cup. You sell a total of 100 cups for $240. Write a system of equations to find the number of x cups of lemonade and y cups of orange juice.

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**Solve the system by substitution**

_______cups lemonade & ______cups orange juice

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Rational Exponents Use the rules for combining fractions when the exponents are rational numbers X 2 3 X 1 2 (()) = X 2 3 + 1 2 = X 4 6 + 3 6 = X 7.

Rational Exponents Use the rules for combining fractions when the exponents are rational numbers X 2 3 X 1 2 (()) = X 2 3 + 1 2 = X 4 6 + 3 6 = X 7.

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