Substitution Worksheet With Answer Key - Waynesville R-Vi School District (Page 27 of 38) in pdf

Substitution Worksheet With Answer Key - Waynesville R-Vi School District Page 27

The exact solution is

which is close, but not equal to,

The solutions to a system will be the same, no matter the method used to solve. However, estimation may need to be

6-2 Substitution

used when graphing the system. To find a precise solution, the preferred method is substitution.

Create a system of equations that has one solution. Illustrate how the system could represent a

real-world situation and describe the significance of the solution in the context of the situation.

Sample answer: Let a = the number of tops Allison bought, and let b = the number of tops Beth bought. Together,

Allison and Beth bought 25 tops. Allison spent $24 per top, and Beth spent $16 per top. Together they spent $464.

How many tops did each girl buy?

a + b = 25

24a + 16b = 464

First, solve the first equation for a to get a = 25

b. Then, substitute 25

b into the second equation.

Use the solution for b and either equation to find a.

So, Allison bought 8 tops, and Beth bought 17 tops.

Explain how to determine what to substitute when using the substitution method of solving

systems of equations.

First, look for a variable that can easily be solved for. An equation containing a variable with a coefficient of 1 can

easily be solved for the variable. That expression can then be substituted into the second equation for the variable.

The debate team plans to make and sell trail mix. They can spend $34.

The pounds of raisins in the mix is to be 3 times the pounds of sunflower seeds. Which system can be used to find r,

the pounds of raisins, and p , pounds of sunflower seeds, they should buy?

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Substitution Worksheet With Answer Key - Waynesville R-Vi School District Page 27