Solving Linear Systems of Equations
and Inequalities by Graphing
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You found a system of equations to represent
Desmond’s missing records situation.
a. How is this system different from the systems
of equations you solved in the last
Exploring?
b. Will this difference prevent you from using a
table and/or a graph to solve the
system?
c. How do you know whether to use slopeintercept form or standard form for the
equations in system of linear equations?
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Sketch the graph of each equation:
𝒙 + 𝒚 = 𝟏𝟐
𝟏𝟓𝒙 + 𝟑𝟎𝒚 = 𝟐𝟒𝟎
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What does this solution tell you about
Desmond’s missing records problem regarding
how many lots of each size were mowed during
the week?
Suppose this time, Desmond charges $20 for the
standard-sized interior lots and $25 for the larger
corner lots. He received a total of $300 for
mowing 14 lots during the past week. Using x to
represent the number of interior lots mowed and
y to represent the number of corner lots mowed,
set up a system of two linear equations to model
this situation.
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The sum of two numbers is 186. The
difference between the same numbers is 32.
Create a system of equations to model the
situation, and then solve the system using a
graphical strategy.
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Dr. Alvarado is a chemist. She needs to mix 10
liters of a solution of a certain chemical that is 64%
pure. (That is, 64% is the chemical, and the rest is
water.) To do this, she will mix a solution that is
70% pure with one that is 50% pure. How many
liters of each should she use?
1) Choose variables and identify what they will
represent.
2) Write a system of equations that Dr. Alvarado
can use to find her answers.
3) Use a table or graph to solve the system.
4) Show how to check your answer. Then write
your answer in a sentence.