91Ó°ÊÓ

Solve each system. If a system's equations are dependent or if there is no solution, state this. $$ \begin{aligned} x-y+z &=4 \\ 5 x+2 y-3 z &=2 \\ 4 x+3 y-4 z &=-2 \end{aligned} $$

Staples recently charged 46.99 per case of regular paper and 61.99 per case of paper made of recycled fibers. Last semester, Valley College Copy Center spent $1433.73 for 27 cases of paper. How many of each type were purchased?

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If \(a\) system has no solution, state this. $$ \begin{aligned} x &=y-1 \\ 2 x &=3 y \end{aligned} $$

Solve each system. If a system's equations are dependent or if there is no solution, state this. $$ \begin{array}{l} {2 u-4 v-w=8} \\ {3 u+2 v+w=6} \\ {5 u-2 v+3 w=2} \end{array} $$

If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. Solve using the substitution method. $$ \begin{aligned} &2 a+6 b=4\\\ &3 a-b=6 \end{aligned} $$

Find the equilibrium point for the following pairs of demand and supply functions. \(D(p)=7500-25 p\) \(S(p)=6000+5 p\)

Solve using matrices. Snack Mix. Bree sells a dried-fruit mixture for \(5.80 per pound and Hawaiian macadamia nuts for \)14.75 per pound. She wants to blend the two to get a 15-lb mixture that she will sell for $9.38 per pound. How much of each should she use?

Solve each system. If a system's equations are dependent or if there is no solution, state this. $$ \begin{array}{l} {4 p+q+r=3} \\ {2 p-q+r=6} \\ {2 p+2 q-r=-9} \end{array} $$

Solve using Cramer's rule. \(\begin{aligned} x-y+2 z &=-3 \\ x+2 y+3 z &=4 \\ 2 x+y+z &=-3 \end{aligned}\)

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If \(a\) system has no solution, state this. $$ \begin{aligned} &a=1+b\\\ &b=5-2 a \end{aligned} $$