91Ó°ÊÓ

Plot the points and draw line segments connecting the points to create the polygon. Then write a system of linear inequalities that defines the polygonal region. Triangle: \((0,0),(-7,0),(-3,5)\)

Use the substitution method to solve the linear system. $$\begin{aligned} &x+y=12\\\ &x+\frac{3}{2} y=\frac{3}{2} \end{aligned}$$

Use linear combinations to solve the system of linear equations. $$\begin{aligned} &3 p-2=-q\\\ &-q+2 p=3 \end{aligned}$$

Graph and check to solve the linear system. $$ \begin{aligned} &\frac{1}{5} x+\frac{3}{5} y=\frac{12}{5}\\\ &-\frac{1}{5} x+\frac{3}{5} y=\frac{6}{5} \end{aligned} $$

Use the following information. A carpenter is buying supplies for a job. The carpenter needs 4 sheets of oak paneling and 2 sheets of shower tileboard. The carpenter pays 99.62 dollars for these supplies. For the next job the carpenter buys 12 sheets of oak paneling and 6 sheets of shower tileboard and pays 298.86 dollars. If the carpenter later spends a total of 139.69 dollars for 1 sheet of shower tileboard and 8 sheets of oak paneling, could you find how much 1 sheet of oak paneling costs? Explain.

Solve the linear system. $$ \begin{aligned} &x-y=-4\\\ &2 y+x=5 \end{aligned} $$

Solve the linear syst$$ \begin{aligned} &x+2 y=8\\\ &3 x-2 y=8 \end{aligned} $$em.

Plot the points and draw line segments connecting the points to create the polygon. Then write a system of linear inequalities that defines the polygonal region. Trapezoid: \((-1,1),(1,3),(4,3),(6,1)\)

Use the substitution method to solve the linear system. $$\begin{aligned} &7 g+h=-2\\\ &g-2 h=9 \end{aligned}$$

Graph and check to solve the linear system. $$ \begin{aligned} &\frac{3}{4} x-\frac{1}{4} y=-\frac{1}{2}\\\ &\frac{1}{4} x-\frac{3}{4} y=\frac{3}{2} \end{aligned} $$