Solving systems with graphing and 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 two lines are parallel when given their equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

What is the solution to a system of equations?

Back

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

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 back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the lines or curves that represent each equation on a coordinate plane.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

What is the first step in solving a system of equations using substitution?

Back

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

Front

How do you find the intersection point of two lines graphically?

Back

To find the intersection point of two lines graphically, plot both lines on a coordinate plane and identify the point where they cross.

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.