Solving Systems of Linear Equations and Inequalities

What results in a system of equations having exactly one solution?

• Lines with the same slope and the same y-intercept

• Lines that are identical

• Lines with different slopes

• Lines with the same slope and different y-intercepts

What scenario leads to a system of equations having no solution?

• Lines that are identical

• Lines with the same slope and different y-intercepts

• Lines that intersect at one point

• Lines with different slopes

In the substitution method, what is the first step?

• Multiply one equation by a constant

• Eliminate one variable

• Isolate a variable in one equation

• Add the two equations together

What is the purpose of multiplying an equation by a constant in the elimination method?

• To isolate a variable

• To find the value of y

• To simplify the equation

• To create matching or opposite coefficients

How do you determine the price of an item in a word problem involving systems of equations?

• By graphing the equations

• By using the substitution method

• By solving the system using elimination or substitution

• By isolating a variable

What does a system of equations represent in a real-world problem?

• The slope of a line

• Relationships between different quantities

• A set of mathematical operations

• A graphical representation

When graphing a system of inequalities, what does shading below the line indicate?

• The line is solid

• Y is less than the expression

• Y is greater than the expression

• The solution set is above the line

What does a solid line in a graph of an inequality represent?

• The inequality does not include the line

• The inequality includes the line itself

• Y is less than the expression

• Y is greater than the expression

How do you convert a standard form equation to slope-intercept form for graphing inequalities?

• By adding or subtracting terms

• By dividing each term by the coefficient of y

• By isolating y on one side of the equation

• By multiplying each term by the coefficient of x

What indicates the solution set in a graph of a system of inequalities?

• The area above the solid line

• The area below the dashed line

• The area shaded by both inequalities

• The area not shaded by either inequality