Exam 5: Coordinate Geometry and Linear Systems

Solve each system by using either the substitution or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } - 4 ( x + 2 ) + 7 ( y - 5 ) = - 65 \\5 ( x + 6 ) - 7 ( y + 4 ) = 19\end{array} \right)$

Solve the system by using the substitution method. $\left( \begin{array} { l } y = - 4 x - 2 \\8 x - 2 y = - 60\end{array} \right)$

Use the slope-intercept form to graph the following line. $y = - \frac { 7 } { 4 } x + 6$

Solve the system by using the substitution method. $\left( \begin{array} { c } 2 x - 6 y = - 8 \\3 x - 9 y = - 12\end{array} \right)$

Use the graphing method to solve the system. $\left( \begin{array} { l } 3 x + 4 y = 11 \\4 x - y = 21\end{array} \right)$ Please enter your answer as values of x and y , separated by a comma.

Determine the slope of the line represented by the given equation. 3 x + 4 y = 0

Find the slope of the line determined by this pair of points. (-7, 9), (-12, 34)

Match the following inequalities with the corresponding graph. -

Solve the problem below by setting up and solving a system of two linear equations in two variables. Suppose that a library buys a total of 32 books, which cost $452. Some of the books cost $21 each and the rest cost $10 per book. How many books of each price did the library buy?

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } y = - 3 x \\y - 3 x = 0\end{array} \right)$

Suppose that the daily profit from an ice cream stand is given by the equation $p = 4 n - 1$ , where $\eta$ represents the number of gallons of ice cream mix used in a day, and $p$ represents the number of dollars of profit. Label the horizontal axis $\eta$ and the vertical axis $p$ , and graph the equation $p = 4 n - 1$ for nonnegative values of $n$ .

Use the elimination-by-addition method to solve the system. $\left( \begin{array} { c } 16 x - 6 y = - 8 \\12 x + 3 y = - 1\end{array} \right)$

Find the equation of the line with the given slope and y -intercept. Leave your answer in slope-intercept form. $m = - \frac { 1 } { 5 } \text { and } b = - 4$

Solve the system by using the substitution method. $\left( \begin{array} { c } 4 x + y = 40 \\5 x - y = 41\end{array} \right)$ Please enter your answer as an ordered pair in the form ( x , y ).

The graph of $y = 2 x$ is a parabola.

Match the equations with their graphs. -

Write the equation of the line that satisfies the given condition: contains the origin and is perpendicular to the line 8 x - 9 y = -5.

Find the equation for the graph.

Find the slope of the line determined by this pair of points. (-10, 6), (-7, 18)

Solve the system using the elimination-by-addition method. $\left( \begin{array} { c } 5 x + 3 y = 19 \\2 x - 4 y = - 8\end{array} \right)$