Exam 8: Systems of Equations and Inequalities

Solve Problems Using Systems of Linear Equations -A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 3 bags of potato chips for $\$ 12.75$ . Another customer buys 2 hot dogs and 2 bags of potato chips for $\$ 7.00$ . Find the cost of each item.

Write the word or phrase that best completes each statement or answers the question. -The Jillson's have up to $\$ 75,000$ to invest. They decide that they want to have at least $\$ 40,000$ invested in stable bonds yielding $6 \%$ and that no more than $\$ 20,000$ should be invested in more volatile bonds yielding $12 \%$ . (a) Using $x$ to denote the amount of money invested in the stable bonds and $y$ the amount invested in the more volatile bonds, write a system of linear inequalities that describe the possible amounts of each investment. (b) Graph the system of inequalities.

Solve Problems Using Systems of Linear Equations -In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. Let $x$ represent the number of years since 1990 and y represent the percentage of women in Milton Lake who smoke. The graph of $y$ against $x$ includes the data points $( 0,16.4 )$ and $( 14,20.32 )$ . Let $x$ represent the number of years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph of $y$ against $x$ includes the data points $( 0,28.3 )$ and $( 10,26.2 )$ . Determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time? [Hint: first find the slope-intercept equation of the line that models the percentage, $\mathrm { y }$ , of women who smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, $y$ , of men who smoke x years after 1990]

Solve Systems of Linear Equations in Three Variables - x+y =-2 3x+5y+3z =-18 x-z =3

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (-1,5,1) x+y+z=5 x-y+5z=-1 2x+y+z=4

Solve Nonlinear Systems By Addition - -3-1=0 4+3-19=0

Solve Nonlinear Systems By Addition - $x ^ { 3 } + y = 0$ $5 x ^ { 2 } - y = 0$

Solve Linear Systems by Addition - -3x+7y=24 -5x-4y=-7

Solve Problems Using Systems in Three Variables -A real estate investor is examining a triangular plot of land. She measures each angle of the field. The sum of the first and second angles is $60 ^ { \circ }$ more than the measure of the third angle. If the measure of the third angle is subtracted from the measure of the second angle, the result is twice the measure of the first angle. Find the measure of each angle. (Note: The sum of the angles of a triangle is $180 ^ { \circ }$ .)

Graph the inequality. - $x + y < - 6$

Solve Problems Using Systems of Linear Equations -More than how many binoculars must be produced and sold for the company to have a profit gain?

Graph the inequality. - $- 2 x - 4 y \leq - 8$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - 7 x + 2 } { ( x - 1 ) ^ { 3 } }$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - -x+6y<-30 x\geq-4

Write the partial fraction decomposition of the rational expression. - $\frac { 4 x ^ { 3 } + 24 x - 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Solve Nonlinear Systems By Addition - -=25 4+25=100

Write the partial fraction decomposition of the rational expression. - $\frac { - 11 x - 34 } { ( x - 2 ) ^ { 2 } \left( x ^ { 2 } + 3 \right) }$

Solve Problems Using Systems in Three Variables -You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds. Consider the following data: x, seconds after ball is thrown y, ball's height, in feet, above the ground 1 84 2 116 4 84 Find the quadratic function $y = a x ^ { 2 } + b x + c$ whose graph passes through the given points.

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - x+y=-1 x-y=17

Write the partial fraction decomposition of the rational expression. - $\frac { 5 x ^ { 2 } + 9 x - 26 } { x ^ { 3 } + 5 x ^ { 2 } + 2 x + 10 }$