Flashcard Review: Substitution and Graphing

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into both equations. If both equations are satisfied (true), then the point is a solution.

Front

What does it mean for two lines to intersect on a graph?

Back

When two lines intersect on a graph, it means that there is a unique solution to the system of equations represented by those lines, which is the point of intersection.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

What is the solution to a system of equations when the lines are parallel?

Back

If the lines are parallel, there is no solution to the system of equations because the lines never intersect.

Front

What is the solution to a system of equations when the lines are coincident?

Back

If the lines are coincident, there are infinitely many solutions because every point on the line is a solution to the system.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form (y = mx + b), identify the y-intercept (b) and use the slope (m) to find another point on the line.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x) between two points on the line.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you solve a system of equations by graphing?

Back

To solve a system of equations by graphing, plot both equations on the same coordinate plane and identify the point(s) where the lines intersect.