Systems: Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a solution?

Back

A solution is a set of values for the variables that makes all equations true.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you solve the system: y = 5x and 3x + y = 24?

Back

Substitute y in the second equation: 3x + 5x = 24, then solve for x.

Front

What is the solution to the system: y = 5x and 3x + y = 24?

Back

(3, 15)

Front

How do you solve the system: x - y = 6 and x = 11?

Back

Substitute x = 11 into the first equation: 11 - y = 6, then solve for y.

Front

What is the solution to the system: x - y = 6 and x = 11?

Back

(11, 5)

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations.

Front

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

Back

It means the lines are parallel and never intersect.

Front

What is the solution to the system: y = 2x + 1 and 3x + y = 16?

Back

(3, 7)