Substitution Method

Name:

Class:

Date:

Show your work for each problem.

1.
In the system $\begin{cases} y = 2x + 3 \\ x + y = 9 \end{cases}$ , what expression should you substitute for $y$ in the second equation?
1. a) $x + 3$
2. b) $2x - 3$
3. c) $2x + 3$
4. d) $9 - x$
2.
If $y = 5$ and $x + y = 12$ , what is $x$ ?
3.
Which variable is easiest to isolate in the equation $x + 3y = 15$ ?
1. a)Both are equally easy
2. b) $y$ (coefficient is 3)
3. c) $x$ (coefficient is 1)
4. d)Neither can be isolated
4.
Solve the system: $\begin{cases} y = x + 2 \\ x + y = 10 \end{cases}$
5.
Solve for $x$ : $\begin{cases} y = 3x \\ 2x + y = 15 \end{cases}$
6.
Solve the system: $\begin{cases} x + y = 8 \\ 2x - y = 7 \end{cases}$
7.
A student substituted $y = 2x + 1$ into $3x + y = 10$ and wrote: " $3x + 2x + 1 = 10$ , so $5x = 10$ , $x = 2$ ". What error was made?
1. a)The 1 was not subtracted from both sides: $5x + 1 = 10$ gives $5x = 9$ , so $x = 1.8$
2. b)Wrong substitution: $y$ should have been replaced by $2x - 1$
3. c)The student should have isolated $x$ first
4. d)No error: the solution is correct
8.
Solve for $y$ : $\begin{cases} x = 2y - 1 \\ 3x + y = 11 \end{cases}$
9.
Solve the system: $\begin{cases} 2x + y = 11 \\ x - y = 1 \end{cases}$
10.
Solve for $x$ : $\begin{cases} y = 4 - x \\ 3x + 2y = 10 \end{cases}$
11.
When you substitute and get $0 = 0$ , what does this mean about the system?
1. a)No solution (parallel lines)
2. b)Exactly one solution
3. c)Infinitely many solutions (same line)
4. d)The calculation has an error
12.
Solve the system: $\begin{cases} 3x + 2y = 12 \\ x - y = 1 \end{cases}$
13.
If $\begin{cases} y = 2x - 5 \\ 4x + 3y = 15 \end{cases}$ , what is the value of $x + y$ ?
14.
Solve the system: $\begin{cases} 2x - 3y = 5 \\ x + 2y = -1 \end{cases}$
15.
A store sold 60 items for a total of 800 euros: T-shirts at 10 euros each and jeans at 20 euros each. Let $t$ be the number of T-shirts and $j$ the number of jeans. Which system describes this situation?
1. a) $\begin{cases} t - j = 60 \\ 10t - 20j = 800 \end{cases}$
2. b) $\begin{cases} t + j = 60 \\ 20t + 10j = 800 \end{cases}$
3. c) $\begin{cases} t + j = 800 \\ 10t + 20j = 60 \end{cases}$
4. d) $\begin{cases} t + j = 60 \\ 10t + 20j = 800 \end{cases}$
16.
Solve: A parking lot has cars and motorcycles. There are 50 vehicles and 160 wheels total. Cars have 4 wheels, motorcycles have 2. How many of each?