This document contains homework questions and examples about solving systems of equations using substitution. It includes: 1) A race between Demitri and Yakov with distance-time graphs and questions about their speeds and when Yakov overtakes Demitri. 2) Three examples walking through the substitution method to solve systems of equations step-by-step. The examples find the intersection point of lines and solve systems algebraically. 3) Questions checking understanding of what it means for something to be a solution to a system of equations and what the solution represents.

1. Opener
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2. Homework Questions:
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4. Day #4: Section 4.10: Solving Systems: Substitution
Demitri & Yakov's Race Demitri and Yakov run around a track. Their distance‐
on the first day of time graph is below.
practice: (Ex. #1)
a. Who is running faster?
b. At what time does Yakov overtake Demitri?
c. At what distance does Yakov overtake Demitri?
d. What are both runners' speeds?
e. Write an equation for Yakov's graph.
f. Write an equation for Demitri's graph.
Solving a System with g. Write an equation that can be used to find the time
Substitution! when Yakov overtakes Demitri. Solve the equation.
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5. Demitri & Yakov's Race Demitri and Yakov practice again the third day. Their
on the third day of distance‐time graph is below.
practice: (Ex. #2)
a. When does Yakov overtake
Demitri in the race?
b. Do the two graphs intersect? Explain.
c. Where would the line of the two graphs intersect?
d. Can two different lines intersect at more than one point?
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6. TOPIC ONE: Think back: What does it mean to be a solution to two
Solving Systems of equations?
Equations by
Substitution: (Ex. # 1)
We are going to use substitution to solve a
system of equations. Find a common solution for the system
of equations below:
y + 2x = 6 and 5x + 2y = 8
Step 1: Choose which variable (or expression) you are going
to substitute for.
Step 2: Solve one of the equations for that variable/
expression.
Step 3: Substitute what your variable/expression equals into
the original equation wherever you see that variable/
expression.
Step 4: Solve your new equation using basic moves.
Step 5: Substitute what the variable equals into either
equation to solve for the other variable.
Step 6: Check your work by substituting in both variable
values into each equation.
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7. Solving Systems of Use substitution to find the intersection point of the graphs
Equations by of 3(y‐1) = 2(x+1) and .25(y‐1)= 1(x ‐ .25).
Substitution: (Ex. # 2)
Step #1:
Step #2:
Step #3:
Step #4:
Step #5:
Step #6:
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8. Solving Systems of What is the solution to the following system of equations?
Equations by If there is no solution, explain.
Substitution: (Ex. # 3) x ‐ 3y = 6
2y + 4x = ‐4
It's your turn!
Step # 1 Result:
Step # 2 Result:
Step # 3 Result:
Step #4 Result:
Step #5 Result:
Step # 6 Result:
Think back: What does this solution represent?
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