Solving Systems by Graphing and Substitution

Front

What is a system of linear equations?

Back

A set of 2 or more equations that have the same variables.

Front

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

Back

It means that the solution (x, y) to the system of equations is the point where the two lines meet.

Front

Solve the system: x - 3y = -13 and 4x + 2y = 4.

Back

(-1, 4)

Front

Solve the system: -5x - 4y = -9 and y = 6.

Back

(-3, 6)

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Front

Solve the system: −3x − 3y = 3 and y = −5x − 17.

Back

(-4, 3)

Front

What is the graphical method of solving systems of equations?

Back

Plotting both equations on a graph and identifying their intersection point.

Front

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

Back

It means there is no solution, as the lines never intersect.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

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

Back

Solve one of the equations for one variable.