Solving Systems by 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 does it mean to solve a system by substitution?

Back

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

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 4x + y = 11, how do you solve them by substitution?

Back

Substitute y from the first equation into the second: 4x + (2x + 3) = 11, then solve for x.

Front

What is the solution to the system of equations y = 2x + 3 and 4x + y = 11?

Back

The solution is (x, y) = (1, 5).

Front

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

Back

A system has no solution if the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

What is the substitution method used for?

Back

The substitution method is used to find the values of variables that satisfy all equations in a system.

Front

How can you check your solution after solving a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.