Question 1

Which of the following best describes the graphical method for solving a system of linear equations?

Accepted Answer

Solve each equation for $y$, plot both lines, and identify their intersection point.

Question 2

Given the system: $x - y = 4$ and $x + y = 12$, what is the solution using the substitution method?

Accepted Answer

$x = 8, y = 4$

Question 3

Which scenario indicates that a system of equations has no solution when using the graphical method?

Accepted Answer

The lines are parallel and never intersect.

Question 4

Solve the following system using the elimination method: $2x + 6y = 18$ and $3x - y = 2$.

Accepted Answer

$x = 3, y = 2$

Question 5

If you invest $8000$ between two accounts paying $3\%$ and $5\%$ annual interest, and the total interest earned after one year is $340$, how much was invested at each rate?

Accepted Answer

$3000$ at $3\%$, $5000$ at $5\%$

Question 6

A coffee grinder charges $11$ per pound for Kenyan French Roast and $10$ per pound for Sumatran coffee. How much of each type should be used to make a $20$-pound blend that sells for $10.35$ per pound?

Accepted Answer

$7$ pounds Kenyan, $13$ pounds Sumatran

Question 7

A riverboat travels $54$ km downstream in $2$ hours and $36$ km upstream in $3$ hours. What is the speed of the boat in still water?

Accepted Answer

$21$ km/h

Question 8

Which of the following is a necessary first step when using the substitution method to solve a system of equations?

Accepted Answer

Solve one equation for one variable in terms of the other.

Question 9

If the elimination method results in a false statement such as $0 = 5$, what does this indicate about the system?

Accepted Answer

The system has no solution.

Question 10

Given the system $0.3x + 0.5y = 1.9$ and $0.5x + 0.3y = 2.1$, what is the value of $x$?

Accepted Answer

$x = 3$

Question 11

Which of the following best describes a system of equations with infinitely many solutions?

Accepted Answer

The equations represent the same line.

Question 12

If you graph two equations and they intersect at $(2, 5)$, what does this point represent?

Accepted Answer

The solution to the system of equations.

Solving Systems of Linear Equations: Methods and Applications

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