Solving Systems with 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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in the context of solving equations?

Back

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

Front

How do you isolate a variable in an equation?

Back

Rearranging the equation to get the variable on one side and the constants on the other.

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

If x = 3y, what is y in terms of x?

Back

y = x/3.

Front

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

Back

(0, 4).

Front

What does it mean if two lines intersect at a point?

Back

The system of equations has one unique solution at that point.

Front

What is the graphical representation of a system of equations?

Back

The lines of the equations plotted on a coordinate plane.

Front

What does it indicate if two lines are parallel?

Back

The system of equations has no solution.