Systems of Equations- Graphing & Substitution

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 to graph a system of equations?

Back

To plot the equations on a coordinate plane and find the point(s) where they intersect.

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 determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the solution to a system of equations?

Back

The point(s) (x, y) where the equations intersect, representing the values that satisfy all equations in the system.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

(2, 5)

Front

What is the value of the y-coordinate of the solution to the system: x - 2y = 1 and x + 4y = 7?

Back

1

Front

What is the solution to the system: 2x - 3y = 6 and 4x + 6y = 12?

Back

No Solution

Front

Solve the system by substitution: y = 2x - 11 and 2x - 8y = 4.

Back

(6, 1)