Question

What is the solution to the above system of equations?

2x+5y=-4
4x-5y=22

A. (3,-2)
B. (13/3, -24/3)
C. (-2,3)
D. (3,2/5)

Answer 1

4.8 Linear Systems UT - P1

For Those of You With 10 Questions and Are on the Same Topic!

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1. What is the apparent solution to the system of equations graphed above?

• A)
  `(-2,2)`

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2. A jet ski company charges a flat fee of $26.00 plus $3.25 per hour to rent a jet ski. Another company charges a fee of $24.00 plus $3.50 per hour to rent the same jet ski. Using a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.

• B)
  `8`

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3. Which graph best represents the solution to the following system?

`\left \{ {{-3x+y < 1} \atop {-x+y\leq 2}} \right.`

• Graph B

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4. A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket. A group of 12 people paid $204.00 for tickets. Which system of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.

• D)
  `\left \{ {{x+y=12} \atop {21.50x+14.75y=204}} \right.`

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5. Which graph best represents the feasibility region for the system shown above?

`\left \{ {{y\geq 2;x\leq 6} \atop {y\leq 3x+2;y\leq -x+10}} \right.`

• Graph A

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6. (Graph Shown in Question)
`\left \{ {{x\leq 8;y\geq 0} \atop {y\leq 3x+2;y\leq -x+10}} \right.`

What is the minimum value for P = x - 2y over the feasibility region defined by the constraints shown above?

• D)
  `-14`

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7. A candy store makes a 13-pound mixture of gummy candy, jelly beans, and hard candy. The cost of gummy candy is $1.00 per pound, jelly beans cost $2.00 per pound, and hard candy costs $2.00 per pound. The mixture calls for three times as many gummy candy pieces as jelly beans. The total cost of the mixture is $20.00. How much of each ingredient did the store use?

• C) 6 lbs. gummy candy, 2 lbs. jelly beans, 5 lbs. hard candy

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8. How many solutions does the following system have?

`\left \{ {{2x+3y=1} \atop {-3x-2y=-1}} \right.`

• C) One Solution

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9. Which linear system of equations does the matrix represent?

[-3 5 | 15 ]

[ 2 3 | -10]

• C)
  `\left \{ {{-3x+5y=15} \atop {2x+3y=-10}} \right.`

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10. What is the solution to the above system of equations?

`\left \{ {{2x+3y=-4} \atop {4x-5y=22}} \right.`

• A)
  `(3,-2)`

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Should be 10/10. Also, good luck on Part 2 guys!

Answer 2

Answer: A. (3,-2)

Explanation:

Solve by Substitution :

// Solve equation [2] for the variable x

[2] 4x = 5y + 22

[2] x = 5y/4 + 11/2

// Plug this in for variable x in equation [1]

[1] 2•(5y/4+11/2) + 5y = -4

[1] 15y/2 = -15

[1] 15y = -30

// Solve equation [1] for the variable y

[1] 15y = - 30

[1] y = - 2

// By now we know this much :

x = 5y/4+11/2

y = -2

// Use the y value to solve for x

x = (5/4)(-2)+11/2 = 3

Solution :

{x,y} = {3,-2}