Solving Systems by Graphing and Substitution

Front

What does the graph of a system of equations with no solution look like?

Back

The graph consists of parallel lines.

Front

What is the solution to the system of equations y = 4x - 2 and y = -x + 3?

Back

The solution is the point (1, 2).

Front

How do you determine the point of intersection of two lines?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.

Front

What is the solution to the system of equations -5x - 4y = -9 and y = 6?

Back

The solution is the point (-3, 6).

Front

What does the point of intersection represent in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

What is the graphical representation of a consistent and independent system of equations?

Back

Two lines that intersect at exactly one point.

Front

What is the solution to the system of equations −3x − 3y = 3 and y = −5x − 17?

Back

The solution is the point (-4, 3).

Front

What does it mean if two lines in a system of equations are coincident?

Back

It means they are the same line and have infinitely many solutions.

Front

How can you use substitution to solve a system of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the significance of the slope in the equations of lines?

Back

The slope indicates the steepness and direction of the line.