Question 1

Solve the system by linear equations by substitution.

Accepted Answer

The answer of Solve the system by linear equations by...

Question 2

Solve the system of linear equations by substitution.

Accepted Answer

The answer of Solve the system of linear equations by...

Question 3

Solve the system of linear equations by substitution.

Accepted Answer

The answer of Solve the system of linear equations by...

Question 4

Solve the system of linear equations by elimination.
2d + 6f = 4
-2d - 5f = -5
A) (5, -1)
B) (-1, 5)
C) (-5, -1)
D) (-1, -5)

Accepted Answer

Adding the two equations directly eliminates d, leading to f = -1. Substituting f = -1 into one of the equations gives d = 5.

Question 5

Solve the system of linear equations by elimination.
7x - 11y = 81
14x - 22y = -162
A) (1, 8)
B) (-1, -8)
C) infinite number of solutions
D) no solution

Accepted Answer

The second equation is a multiple of the first, but with a different constant term, indicating parallel lines with no intersection.

Question 6

Solve the system of linear equations by elimination.
-4x - 3y = -2
-8x + 9y = 86
A) (4, -6)
B) (-6, 4)
C) (6, -4)
D) (-4, 6)

Accepted Answer

The answer of Solve the system of linear equations by...

Question 7

Solve the system of linear equations by elimination.
5t + 13q = -84
15t + 7q = 4
A) (-4, -8)
B) (4, -8)
C) (-8, 4)
D) (-8, -4)
E) None of the above.

Accepted Answer

The answer of Solve the system of linear equations by...

Question 8

Solve the system by linear equations by elimination.

Accepted Answer

The answer of Solve the system by linear equations by...

Question 9

Solve the system of linear equations by elimination.

Accepted Answer

The answer of Solve the system of linear equations by...

Question 10

Solve the system of linear equations by elimination.

Accepted Answer

The answer of Solve the system of linear equations by...

Question 11

Solve the system of linear equations by graphing the following equations.
7x + 6y = 63
8x + 5y = 59
A) (3, 7)
B) (7, 3)
C) (-3, 7)
D) (3, -7)

Accepted Answer

The solution to the system of equations is the point where the two lines intersect. By graphing the equations, the intersection point is found to be (3, 7).

Question 12

Solve the system of linear equations by graphing the following equations.
-8x + 8y = -16
-7x + 2y = 16
A) (-6, -4)
B) (-4, -6)
C) (4, -6)
D) (-6, 4)

Accepted Answer

The answer of Solve the system of linear equations by...

Question 13

Solve the system of linear equations by graphing the following equations.
4x - 6y = -52
-5x + 5y = 55
A) (4, -7)
B) (-7, 4)
C) (4, -5)
D) (-52, 55)

Accepted Answer

The answer of Solve the system of linear equations by...

Question 14

Solve the system of linear equations by graphing the following equations.
4x - 5y = 55
7x - 2y = 49
A) (5, -7)
B) (-7, 5)
C) (7, 5)
D) (5, 7)

Accepted Answer

The answer of Solve the system of linear equations by...

Question 15

Starbucks Coffee sells its House Blend for $9.08 per pound and its Sumatra coffee for $13.97 per pound. How many pounds of each type of coffee did a Starbucks outlet sell in one day if the total number of pounds sold was 50 and the day's receipts totaled $674.05? Let h represent the number of pounds of House Blend and s the number of pounds of Sumatra sold. Round your answer to the nearest pound.
A) h = 45 pounds, s = 5 pounds
B) h = 5 pounds, s = 45 pounds
C) h = 35 pounds, s = 15 pounds
D) h = 15 pounds, s = 35 pounds

Accepted Answer

To solve this, set up two equations based on the given information: $h + s = 50$ (total pounds sold) and $9.08h + 13.97s = 674.05$ (total sales). Solving these equations simultaneously, you find that $h = 5$ and $s = 45$, meaning 5 pounds of House Blend and 45 pounds of Sumatra were sold.

Question 16

A health food company mixes dried fruit with walnuts to make a trail mix blend. How many pounds of each ingredient must be mixed if dried fruit sells for $7.71 per pound, walnuts sell for $2.51 per pound, and the company produces 45 pounds per batch valued at $242.95? Let d represent the number of pounds of dried fruit and w the number of pounds of walnuts.
A) d = 10 pounds, w = 35 pounds
B) d = 35 pounds, w = 10 pounds
C) d = 20 pounds, w = 25 pounds
D) d = 25 pounds, w = 20 pounds

Accepted Answer

The equations are: d + w = 45 and 7.71d + 2.51w = 242.95. Solving these gives d = 25 and w = 20.

Question 17

A catering company mixes cooked shredded beef with roasted Anaheim chilies to use as the filling in their house specialty burrito. How many pounds of both shredded beef that sells for $6.61 per pound and chilies that sell for $1.59 per pound must be mixed to produce 85 pounds of the mixture, witch sells for $511.65? Let b represent the number of pounds of beef and c represent the number of pounds of chilies.
A) b = 10 pounds, c = 75 pounds
B) b = 75 pounds, c = 10 pounds
C) b = 50 pounds, c = 35 pounds
D) b = 35 pounds, c = 50 pounds

Accepted Answer

The total cost of the mixture is $511.65, and the total weight is 85 pounds. Using the equation 6.61b + 1.59c = 511.65 and b + c = 85, solving these equations simultaneously gives b = 75 pounds and c = 10 pounds.

Question 18

A candy company mixes chocolate and peanuts to create one of their signature confections. How many pounds of chocolate costing $13.50 per pound must be mixed with peanuts costing $3.69 per pound to create 60 pounds of mixture that costs $662.85? Let c represent the number of pounds of chocolate and p represent the number of pounds of peanuts.

Accepted Answer

The answer of A candy company mixes chocolate and peanuts...

Question 19

In chemistry lab, Bevan has to make a 495 milliliter solution that is 12% HCl. All that is in the lab is 2% and 20% HCl. How many milliliters of each solution should he use to obtain the desired mix?

Accepted Answer

The answer of In chemistry lab, Bevan has to make...

Question 20

Leticia has been tacking two volatile stocks. Stock A over the last year has increased 7%, and stock B has increased 10% (using a simple interest model). She has $14,300 to invest and would like to split it between the two stocks. If the stocks continue to perform the same rate, how much should she invest in each to result in a balance of $15,559.

Accepted Answer

The answer of Leticia has been tacking two volatile stocks....

Quiz 8: Systems of Linear Equations and Inequalities

Solve the system by linear equations by substitution.

Solve the system of linear equations by substitution.

Solve the system of linear equations by substitution.

Solve the system of linear equations by elimination. 2d + 6f = 4 -2d - 5f = -5

Solve the system of linear equations by elimination. 7x - 11y = 81 14x - 22y = -162

Solve the system of linear equations by elimination. -4x - 3y = -2 -8x + 9y = 86

Solve the system of linear equations by elimination. 5t + 13q = -84 15t + 7q = 4

Solve the system by linear equations by elimination.

Solve the system of linear equations by elimination.

Solve the system of linear equations by elimination.

Solve the system of linear equations by graphing the following equations. 7x + 6y = 63 8x + 5y = 59

Solve the system of linear equations by graphing the following equations. -8x + 8y = -16 -7x + 2y = 16

Solve the system of linear equations by graphing the following equations. 4x - 6y = -52 -5x + 5y = 55

Solve the system of linear equations by graphing the following equations. 4x - 5y = 55 7x - 2y = 49

In chemistry lab, Bevan has to make a 495 milliliter solution that is 12% HCl. All that is in the lab is 2% and 20% HCl. How many milliliters of each solution should he use to obtain the desired mix?