Systems of Equations --- 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 solve a system of equations?

Back

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

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 isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in using the substitution method?

Back

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

Front

If y = 2x + 3, what is y when x = 2?

Back

y = 2(2) + 3 = 7.

Front

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

Back

Substituting y = 2 into the first equation gives 2x + 3(2) = 6, so x = 0. Solution is (0, 2).

Front

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

Back

The system of equations has one unique solution, which is the coordinates of the intersection point.

Front

What does it mean if two lines are parallel?

Back

The system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines coincide?

Back

The system of equations has infinitely many solutions, as the lines are the same.