Solving Systems by Substitution #1

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 substitution method?

Back

The substitution method is a technique for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

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

Back

The solution is (2, 0).

Front

What is the solution to the system: y = -2x + 18 and y = 8?

Back

The solution is (5, 8).

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

What is the solution to the system: x = -3y - 8 and x - 2y = -3?

Back

The solution is (-5, -1).

Front

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

Back

The solution is (0, 1).