✅ 8th Grade Math (Algebra I): Systems of Linear Equations Quiz
✅ 8th Grade Math (Algebra I): Systems of Linear Equations Quiz
Which ordered pair $(x, y)$ is a solution to the system of equations below?
$$
\begin{cases}
y = x + 1 \\
y = 3
\end{cases}
$$
B) $(3, 2)$
C) $(1, 3)$
D) $(3, 1)$
Consider the system of equations:
$$
\begin{cases}
x = 5 \\
y = 2x - 7
\end{cases}
$$
What is the value of $y$ in the solution to this system?
B) $5$
C) $-2$
D) $17$
Solve the following system of equations by substitution:
$$
\begin{cases}
y = x + 5 \\
2x + y = 11
\end{cases}
$$
B) $(2, 7)$
C) $(3, 8)$
D) $(4, 9)$
Solve the system of equations by elimination:
$$
\begin{cases}
x + y = 10 \\
x - y = 4
\end{cases}
$$
B) $(7, 3)$
C) $(5, 5)$
D) $(8, 2)$
A store sells two types of shirts: T-shirts for 10 each and polo shirts for 20 each. On a particular day, the store sold a total of 15 shirts and made 200. How many T-shirts were sold?
A) 5B) 8
C) 10
D) 12
The graph of two linear equations is shown below. What is the solution to the system of equations?
(Imagine a graph where two lines intersect at the point (4, 1))
B) $(-4, 1)$
C) $(4, 1)$
D) $(4, -1)$
Solve the following system of equations:
$$
\begin{cases}
2x + y = 7 \\
3x - 2y = 0
\end{cases}
$$
B) $(3, 1)$
C) $(1, 5)$
D) $(4, -1)$
What is the solution to the system of equations below?
$$
\begin{cases}
3x + 2y = 13 \\
x - 4y = -5
\end{cases}
$$
B) $(2, 3)$
C) $(1, 5)$
D) $(5, -1)$
A local café sells coffee for 2.50 per cup and tea for 1.75 per cup. In one hour, they sold 20 drinks and collected 43.75. How many cups of coffee and how many cups of tea did they sell?
A) 10 coffee, 10 teaB) 15 coffee, 5 tea
C) 13 coffee, 7 tea
D) 7 coffee, 13 tea
For which system of equations is $(0, 2)$ the solution?
A) $$ \begin{cases} y = x + 2 \\ y = 2x + 1 \end{cases} $$B) $$ \begin{cases} y = 2x + 2 \\ y = -x + 2 \end{cases} $$
C) $$ \begin{cases} y = 3x - 2 \\ y = x + 2 \end{cases} $$
D) $$ \begin{cases} y = -x + 2 \\ y = x - 2 \end{cases} $$
What is the solution to the system of equations?
$$
\begin{cases}
y - 3x = -1 \\
2y + 5x = 9
\end{cases}
$$
B) $(2, 5)$
C) $(3, 8)$
D) $(0, -1)$
Two angles are supplementary, meaning their measures sum to 180 degrees. If the measure of one angle is 12 degrees less than twice the measure of the other angle, what are the measures of the two angles?
A) 64 degrees and 116 degreesB) 56 degrees and 124 degrees
C) 60 degrees and 120 degrees
D) 72 degrees and 108 degrees
A chemist has two solutions of acid. One solution is 20% acid, and the other is 50% acid. She wants to mix them to get 10 liters of a 30% acid solution. How many liters of the 20% acid solution should she use?
A) 5 litersB) $6\frac{2}{3}$ liters
C) $3\frac{1}{3}$ liters
D) 7 liters
Consider the system of equations:
$$
\begin{cases}
6x - 2y = 10 \\
9x - 3y = 15
\end{cases}
$$
How many solutions does this system have?
B) No solution
C) Infinitely many solutions
D) Two solutions
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