91Ó°ÊÓ

Determine whether the following statement is true or false. A solution of \(a\) system of linear inequalities is an ordered pair that is a solution of any one of the inequalities in the system. Explain.

Describe the graph of a linear system that has the given number of solutions. Sketch an example. infinitely many solutions

Use the graph-and-check method to solve the system of linear equations. $$ \begin{aligned} &y=-2 x+3\\\ &y=x-3 \end{aligned} $$

Tell which equation you would use to isolate a variable. Explain your reasoning. $$\begin{aligned} &m+4 n=30\\\ &m-2 n=0 \end{aligned}$$

Tell which equation you would use to isolate a variable. Explain your reasoning. $$\begin{aligned} &5 c+3 d=11\\\ &5 c-d=5 \end{aligned}$$

Graph the system of linear inequalities. \(x+y<4\) \(x+y>-2\)

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$ \begin{aligned}&4 x+4 y=-8\\\&2 x+2 y=-4\end{aligned} $$

Use the substitution method to solve the linear system. $$\begin{aligned} &2 x+3 y=31\\\ &y=x+7 \end{aligned}$$

Use the substitution method to solve the linear system. $$\begin{aligned} &x-y=0\\\ &12 x-5 y=-21 \end{aligned}$$

Choose a method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{aligned} &x+2 y=2\\\ &x+4 y=-2 \end{aligned} $$