Solving Systems by Substitution

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 system of equations has no solution?

Back

A system of equations has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check your solution by substituting the values of the variables back into the original equations to see if they satisfy both equations.

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 point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

Front

How do you solve the equation y = 2x + 1 for x?

Back

To solve for x, you can rearrange the equation to x = (y - 1)/2.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the lines corresponding to each equation plotted on a coordinate plane.

Front

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

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

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

Back

The y-intercept can be found by setting x = 0 in the equation and solving for y.