Intro to Systems of Equations

Intro to Systems of Equations

By Christopher Wells

Mo' money, mo' problems

You recently received some birthday money, $130 to be exact. You count th number of bills you have and find that you have 17 bills, all either $10 or $5 bills.

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How many of each bill do you have?

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Hint: Just try guessing and checking first!​

Poll

Which do you think is correct?

• nine $5 bills and eight $10 bills

• eight $5 bills and nine $10 bills

• ten $5 bills and seven $10 bills

• six $5 bills and eleven $10 bills

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You have nine $10 bills and eight $5 bills.​

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You've lost me.....

Systems of equations are two or more equations that have the same variables like:

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y = x + 1

y = -2x + 6

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which both have an x and a y​

How does this have to do with math?

Sometimes, in math, we are asked for two answers, like how many $5 bills AND $10 bills. Systems of equations are how we solve these problems. ​

Systems of Equations ​

Systems of equations are used when we are given two pieces of information and asked for two answers from it, like our first question.​

Multiple Choice

What kind of equations did we learn to graph and solve last unit?

• nonlinear

• linear

• proportional

Solutions are where two lines intersect on a graph and these are our answers.

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The solutions here is (1, -3) because that is where the lines intersect! ​

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Solutions = answers​

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Multiple Select

WHat is a solution to a system of linear equations?

• The point where both lines intersetct.

• The point where the y-axis and x-axis meet.

• An ordered pair that both lines share.

• A salt dissilved in water.