Exam 4: Systems of Equations and Inequalities

State the number of solutions of the system of linear equations $\left\{ \begin{array} { l } y = 3 x - 7 \\y = 7 x - 3\end{array} \right.$ without solving the system.

The sum of the measures of two angles of a triangle is twice the measure of the third angle. The measure of the second angle is 9^∘ more than the measure of the third angle. Find the measures of the three angles.

Which of the following systems of equations below has the solution (1,4) ? $\left\{ \begin{array} { l } 4 x - 6 y = - 20 \\3 x - 5 y = - 17\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 24 \\3 x - 5 y = 19\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 16 \\3 x - 5 y = 12\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 36 \\3 x - 5 y = 29\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 26 \\3 x - 5 y = 21\end{array} \right. \right. \right. \right. \right.$

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } y \geq - 2 \\y < 2\end{array} \right.$

Use the graphical method to solve the system of equations below. $\left\{ \begin{array} { l } y = x + 2 \\y = - x + 4\end{array} \right.$

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. Round your answer to three decimals places. $\left[ \begin{array} { c c c } 0.3 & 0.4 & - 0.3 \\- 0.4 & 0.2 & - 0.4 \\- 0.7 & 0.2 & - 0.1\end{array} \right]$

Match the system of linear inequalities below with its graph. $\left\{ \begin{array} { l } y < x \\y > - 1 \\x \leq 0\end{array} \right.$

Solve the system of linear equations below by the method of elimination. $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = \frac { 1 } { 9 } \\\\3 x - 4 y = - \frac { 13 } { 3 }\end{array} \right.$

Solve the system of linear equations below by any convenient method. $\left\{ \begin{array} { c } 2 x - 2 y = 2 \\- 2 x + y = - 2\end{array} \right.$

How many liters of a 34% alcohol solution must be mixed with 84% solution to obtain 16 liters of a 71.5% solution?

Use back-substitution to solve the system of linear equations below. $\left\{ \begin{aligned}x - y - z & = 3 \\2 y - z & = - 12 \\z & = - 2\end{aligned} \right.$

Graph the equations in the system. Use the graphs to determine whether the system is consistent or inconsistent. If the system is consistent, determine the number of solutions. $\left\{ \begin{array} { l } 5 x + y = - 8 \\- 5 x - y = 8\end{array} \right.$

Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ for an object that has distance $s = 24 \text { feet }$ at t=1 second, $s = 47 \text { feet }$ at t=2 seconds, and $s = 78 \mathrm { feet }$ at $t = 3$ seconds.

Solve the system of linear equations below by the method of elimination. $\left\{ \begin{array} { c } \frac { 5 } { 6 } b - \frac { 11 } { 12 } m = - \frac { 11 } { 18 } \\\\- \frac { 1 } { 2 } b + \frac { 3 } { 4 } m = \frac { 2 } { 3 }\end{array} \right.$

Use Cramer s Rule to solve the system of linear equations below. $\left\{ \begin{array} { l } - 2 x + 4 y = 18 \\x + 2 y = 11\end{array} \right.$

Write the system of linear equations represented by the augmented matrix below. Use variables x , y , z , v , and w. $\left[ \begin{array} { c c c c : c } - 4 & - 6 & - 7 & 7 & - 9 \\- 4 & - 3 & - 3 & - 7 & 9 \\- 2 & - 1 & - 5 & 7 & - 2 \\- 7 & - 7 & - 7 & - 7 & 3\end{array} \right]$

Form the augmented matrix for the system of linear equations below. $\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.$

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x \geq 1 \\x - 2 y \leq 2 \\3 x + 2 y \geq 5 \\x + y \leq 4\end{array} \right.$

A fundraising dinner was held on two consecutive nights. On the first night, 160 adult tickets and 237 children's tickets were sold, for a total of $3,478.25. On the second night, 193 adult tickets and 314 children's tickets were sold, for a total of $4,399.5. Find the price of each type of ticket.

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x + y \leq 2 \\x - 2 y \geq 0 \\y \geq - 1\end{array} \right.$