Solve 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, perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the first step in solving the system: 3x + 2y = 16 and 7x + y = 19?

Back

The first step is to solve one of the equations for one variable, for example, solve the second equation for y.

Front

What is the solution to the system: 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 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 every point on the line is a solution.

Front

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

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the solution to the system: y = -6x + 5 and -2x + y = 5?

Back

The solution is (0, 5).

Front

What is the solution to the system: x = -3y + 1 and -3x - 3y = -15?

Back

The solution is (7, -2).