1.
Determine if each of the following is a solution to the equation \(4x+3y=12\text{:}\)
-
\(\displaystyle (4,-1)\)
-
\(\displaystyle (0,4)\)
-
\(\displaystyle 3\)
Exercises 6.5 Practice Problems
2.
Determine if each of the following is a solution to the equation \(x-5y=-2\text{:}\)
-
\(\displaystyle (3,1)\)
-
\(\displaystyle (0,0)\)
-
\(\displaystyle \left(\frac{5}{2}, \frac{1}{2}\right)\)
3.
Suppose we have the system of equations:
\begin{equation*}
\begin{cases}
4 \amp= 5x+y\\
-6 \amp= -2x+4y
\end{cases}
\end{equation*}
Check if each of the following is a solution to the system:
-
\(\displaystyle (1,-1)\)
-
\(\displaystyle (2,5)\)
-
\(\displaystyle (-1,9)\)
4.
Suppose we have the system of equations:
\begin{equation*}
\begin{cases}
2 \amp= 3x-2y\\
4 \amp= -2x+4y
\end{cases}
\end{equation*}
Check if each of the following is a solution to the system:
-
\(\displaystyle (1,-2)\)
-
\(\displaystyle (2,2)\)
-
\(\displaystyle (0,0)\)
5.
Suppose we have the system of equations:
\begin{equation*}
\begin{cases}
0 \amp= \frac{1}{2}x-2y\\
12 \amp= 4x-4y
\end{cases}
\end{equation*}
Check if each of the following is a solution to the system:
-
\(\displaystyle (1,-4)\)
-
\(\displaystyle (2,3)\)
-
\(\displaystyle (4,1)\)
6.
Suppose we have the system of equations:
\begin{equation*}
\begin{cases}
-3 \amp= 3x-2y\\
0 \amp= 6x-2y
\end{cases}
\end{equation*}
Check if each of the following is a solution to the system:
-
\(\displaystyle (1,3)\)
-
\(\displaystyle (0,3)\)
-
\(\displaystyle (-2,2)\)
7.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}4 \amp= 4x-2y \\ 3 \amp= 5x-3y\end{cases}
\end{equation*}
8.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}-4 \amp= 2x-y \\ -2 \amp= 4x-3y\end{cases}
\end{equation*}
9.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}0 \amp= x-\frac{1}{2}y \\ -1 \amp= 3x-3y\end{cases}
\end{equation*}
10.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}10 \amp= 5x-2y \\ 2 \amp= x-4y\end{cases}
\end{equation*}
11.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}1 \amp= -3x+2y \\ 5 \amp= x-y\end{cases}
\end{equation*}
12.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}2 \amp= 4x-2y \\ 5 \amp= 2x+3y\end{cases}
\end{equation*}
13.
Solve the following system of equations using substitution:
\begin{equation*}
\begin{cases}-2 \amp= 4x-2y \\ 5 \amp= 2x+3y\end{cases}
\end{equation*}
14.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}4 \amp= 4x-2y \\ 3 \amp= 5x-3y\end{cases}
\end{equation*}
15.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}-4 \amp= 2x-y \\ -2 \amp= 4x-3y\end{cases}
\end{equation*}
16.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}0 \amp= x-\frac{1}{2}y \\ -1 \amp= 3x-3y\end{cases}
\end{equation*}
17.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}10 \amp= 5x-2y \\ 2 \amp= x-4y\end{cases}
\end{equation*}
18.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}1 \amp= -3x+2y \\ 5 \amp= x-y\end{cases}
\end{equation*}
19.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}2 \amp= 4x-2y \\ 5 \amp= 2x+3y\end{cases}
\end{equation*}
20.
Solve the following system of equations using elimination:
\begin{equation*}
\begin{cases}-2 \amp= 4x-2y \\ 5 \amp= 2x+3y\end{cases}
\end{equation*}
21.
Solve the following system of equations:
\begin{equation*}
\begin{cases}-2 \amp= 4x-2y \\ -1 \amp= 2x-y\end{cases}
\end{equation*}
22.
Solve the following system of equations:
\begin{equation*}
\begin{cases}5 \amp= 3x-2y \\ -1 \amp= 4y-6x\end{cases}
\end{equation*}
23.
Solve the following system of equations:
\begin{equation*}
\begin{cases}10 \amp= x-\frac{1}{2}y \\ -24 \amp= 2y-4x\end{cases}
\end{equation*}
24.
Solve the following system of equations:
\begin{equation*}
\begin{cases}6 \amp= 2x-y \\ -12 \amp= 4x-2y\end{cases}
\end{equation*}
25.
Solve the following system of equations:
\begin{equation*}
\begin{cases}6 \amp= 2x-y \\ 12 \amp= 4x-2y\end{cases}
\end{equation*}
26.
Solve the following system of equations:
\begin{equation*}
\begin{cases}16 \amp= 4x-y \\ 8 \amp= 2x-\frac{1}{2}y\end{cases}
\end{equation*}
27.
Solve the following system of equations:
\begin{equation*}
\begin{cases}21 \amp= -3x+7y \\ 7 \amp= -6x+14y\end{cases}
\end{equation*}
