Systems of Equations--Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable on one side of the equation and the constants on the other.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system.

Front

What is the first step in the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you use substitution?

Back

Set 2x + 3 equal to -x + 1 and solve for x: 2x + 3 = -x + 1.

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

The solution is (x, y) = (-2, -1).

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.