Systems of Two Equations
For problems 1-3 without solving, explain how to determine the number of solutions for the systems.
1) \(\begin{cases} y=-2x+3 \\ y=\Large\frac{4}{5}\normalsize x-2 \end{cases}\)
2) \(\begin{cases} 3x-y=5\\ 6x-2y=10\end{cases}\)
3) \(\begin{cases} -10x+7y=11\\ -10x+7y=5\end{cases}\)
4) Create a linear system with two equations that has a solution of \((4, -3)\). Do not use vertical or horizontal lines. You can check to see if your equations work on Desmos.
For problems 1-3 without solving, explain how to determine the number of solutions for the systems.
1) \(\begin{cases} y=-2x+3 \\ y=\Large\frac{4}{5}\normalsize x-2 \end{cases}\)
2) \(\begin{cases} 3x-y=5\\ 6x-2y=10\end{cases}\)
3) \(\begin{cases} -10x+7y=11\\ -10x+7y=5\end{cases}\)
4) Create a linear system with two equations that has a solution of \((4, -3)\). Do not use vertical or horizontal lines. You can check to see if your equations work on Desmos.
For problems 5-11 solve the systems of equations.
5) \(\begin{cases}y=2x+1\\ y=-4x+7\end{cases}\)
6) \(\begin{cases}-5x+8y=14\\ 5x+10y=40\end{cases}\)
7) \(\begin{cases}2x+5y=-4\\ 4x+y=28\end{cases}\)
8) \(\begin{cases}9x=y+2\\ x+3y=-6\end{cases}\)
9) \(\begin{cases}6x-5y=-10\\ -4x-7y=-14\end{cases}\)
10) \(\begin{cases}18x-2y=10\\ -9x+y=-5\end{cases}\)
11) \(\begin{cases}2x+7y=-5\\ -3x-4y=14\end{cases}\)
Systems of Three Equations
For problems 12-17 solve the systems of equations.
12) \(\begin{cases}3x+5z=-1\\ -2x+5z=9\\ x+3y-3z=7\end{cases}\)
13) \(\begin{cases}3y-2z=6\\ 7x-4y+3z=-7\\7x+y-5z=-11\end{cases}\)
14) \(\begin{cases}-8x+2y-3z=10\\ 4x-3y+z=-7\\12y+3z=5\end{cases}\)
15) \(\begin{cases} 4x+3y+z=-11\\ -x+5y+z=-14\\x+3y-z=-18\end{cases}\)
16) \(\begin{cases} 3x-2y+2z=-2\\-3x+4y-6z=-8\\x-6y-2z=-14\end{cases}\)
17) \(\begin{cases} 3x+8y-4z=-2\\2x+4y-7z=6\\6x+2y-8z=-18\end{cases}\)
Review
18) Solve the following equation for \(y\) in terms of \(x\): \(4y-5xy+2x=7\)
19) Write the equation of the line that is parallel to \(2x+4y=-5\) and passes through the point \((4,3)\).
20) Solve: \(\frac{1}{2}\left|5x-4\right|-10=-2\)
Solution Bank