Systems Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you determine the break-even point in a business scenario?

Back

The break-even point is found by setting total revenue equal to total costs and solving for the number of units sold.

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the line on the y-axis.

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure they reflect the problem's constraints.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients represent the relationship between the variables; they indicate how much one variable changes in relation to another.

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is substitution in solving systems of equations?

Back

Substitution involves solving one equation for a variable and then substituting that expression into another equation.

Front

What is elimination in solving systems of equations?

Back

Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.