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

Front

What is the first step in solving the system: y = 2x + 1 and y = 4x - 1?

Back

The first step is to set the two equations equal to each other since they both equal y: 2x + 1 = 4x - 1.

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3).

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 is the solution to the system: 3x + y = 1 and y = 4x + 1?

Back

The solution is (0, 1).

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the values of the variables that satisfy all equations in the system.

Front

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

Back

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

Front

What is the solution to the system: y = -3x + 11 and 5x + y = 21?

Back

The solution is (5, -4).