Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means that the two equations have a common solution, represented by the point where the lines meet.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

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

Back

Substitute the x and y values of the point into both equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a graph, and their intersection point represents the solution.

Front

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

Back

It means that the system has no solution, as the lines never intersect.

Front

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

Back

It means that the system has infinitely many solutions, as the lines lie on top of each other.

Front

Solve using elimination: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

Use substitution to solve: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0)