Exam 4: Systems of Linear Equations and Inequalities

Solve using a system of three linear equations. -A basketball player scored 32 points in a game. The number of three-point field goals the player made was 24 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals The player made was 11 more than the number of three-point field goals made. Find the number of free-throws, Two-point field goals, and three-point field goals that the player made in the game.

Solve the problem. -Julie and Eric row their boat (at a constant speed)32 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the current.

Solve. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is $2 \mathrm { P } + 3 \mathrm {~F} \leq 23$ , where $\mathrm { P }$ is the number of police cars on active duty and $\mathrm { F }$ is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation $4 \mathrm { P } + 2 \mathrm {~F} \leq 34$ is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so $P \geq 0$ and $F \geq 0$ . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for $\mathrm { P }$ and the vertical axis for $\mathrm { F }$ . If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?

Determine whether the given ordered pair is a solution to the system of equations. -(-4, -5) 4x + y = -21 3x + 4y = -32

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. - 7x-5y=4 -14x+10y=-16

Determine whether the given ordered pair is a solution to the system of equations. -(-6, -4) 4x + y = -20 2x + 4y = 4

Choose the most appropriate method for solving the system of equations. Do not solve. -x + y = 3050 4x + 5y = 8170

Graph the system of inequalities. - -2x+y<6 -2x+y>-1