Systems of Equations
Name _____________________________________________________ Date __________________
Score _________
Questions
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1.
Can you find one solution for both equations?
\begin{array}{l}
x + y = 12 \
x - y = 2
\end{array}
Hint: Using graphing, substitution or elimination, find a point, $(x, y)$ that makes both equations true.
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2.
Can you solve this system of equations using elimination?
\begin{array}{l}
x + 2y = 5 \
3x + 2y = 17
\end{array}
Hint: Use subtraction to eliminate the $y$ variable, then solve for $x$.
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3.
Can you solve this system of equations using elimination?
\begin{array}{l}
5x + 2y = -1 \
3x + 7y = 11
\end{array}
Hint: Eliminate $x$ variables by multiplying the first equation by $3$, and the second by $5$. Or, eliminate the $y$ variable by multiplying the first equation by $7$, and the second by $2$. Then subtract.
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4.
Is this an “inconsistent system”?
\begin{array}{l}
y = x - 1 \
-x + y = 2
\end{array}
Hint: Convert both equations to the Slope-Intercept form, and compare their slopes and y-intercepts.
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5.
What is a “consistent” system of equations?
Hint: How many solutions must the system have?
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6.
What is an “inconsistent” system of equations?
Hint: How many solutions must the system have?
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7.
What do we call a system of equations that has infinitely many solutions?
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8.
What are the three classifications of linear systems?
Hint: The classifications are based on three possible types of solutions.
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