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

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept and slope, plot the y-intercept on the graph, and use the slope to find another point.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect and have no solution.

Front

What does it mean for two lines to be coincident?

Back

Two lines are coincident if they lie on top of each other, meaning they have infinitely many solutions.

Front

What is the graphical interpretation of the solution to a system of equations?

Back

The solution to a system of equations is the point(s) where the graphs of the equations intersect.

Front

How can you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y to zero in the equation and solve for x.