Practice - Algebra 1

2.7.5 Practice

2.7.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 – 8, solve each system of equations to determine if there is one solution, no solution, or infinitely many solutions.

$\left\{\begin{array}{rcl}5x\;-\;3y\;&=&\;7\\x\;-\;0.6y\;&=&\;1.4\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-x\;+\;2y\;&=&\;-1\\5x\;-\;10y\;&=&\;6\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}7x+6y&=&2\\-28x-24y&=&-8\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-0.2x\;+\;0.4y\;&=&\;0.6\\x-2y&=&-3\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-0.1x\;+\;0.2y\;&=&\;0.6\\5x-10y&=&1\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}3x+6y&=&11\\\;2x+4y&=&9\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-x+2y=4\\\;2x-4y&=&1\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}3x-2y&=&5\\\;-9x+6y&=&-15\end{array}\right.$

infinitely many solutions
no solution
one solution

Which system of equations has infinitely many solutions?

$\left\{\begin{array}{l}-4x\;+\;3y\;=\;-12\\\;8x\;+\;6y\;=\;-24\end{array}\right.$
$\left\{\begin{array}{l}-4x\;+\;3y\;=\;12\\\;8x\;-\;6y\;=\;\;24\end{array}\right.$
$\left\{\begin{array}{l}4x\;+\;3y\;=\;12\\\;8x\;+\;6y\;=\;12\end{array}\right.$
$\left\{\begin{array}{l}4x\;+\;3y\;=\;12\\\;8x\;+\;6y\;=\;-24\end{array}\right.$

Which system of equations has no solution?

$\left\{\begin{array}{l}9x+21y=270\\\;3x+7y=90\end{array}\right.$
$\left\{\begin{array}{l}3x-7y=15\\\;3x+7y=40\end{array}\right.$
$\left\{\begin{array}{l}3x+7y=15\\\;6x+14y=30\end{array}\right.$
$\left\{\begin{array}{l}3x+7y=15\\\;3x+7y=40\end{array}\right.$