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 set of values that satisfy all equations in the system.

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, you perform inverse operations to get the variable on one side of the equation by itself.

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 make all equations true simultaneously.

Front

What is the first step in using 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 x + y = 10, how would you use substitution?

Back

Substitute y in the second equation: x + (2x + 3) = 10, then solve for x.

Front

What is the solution to the system of equations 2y + x = -15 and x = 3y?

Back

The solution is (-9, -3).

Front

What does it mean if two equations in a system have no solution?

Back

If two equations have no solution, it means they represent parallel lines that never intersect.

Front

What does it mean if two equations in a system have infinitely many solutions?

Back

If two equations have infinitely many solutions, it means they represent the same line, and every point on that line is a solution.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the solution back into the original equations to see if both equations are satisfied.