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 of equations by substitution?

Back

Solving 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 and all other terms on the opposite side.

Front

What is the first step in solving the system of equations y = 2x + 1 and y = 4x - 1 by substitution?

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 of equations y = -2x + 18 and y = 8?

Back

The solution is (5, 8), found by substituting y = 8 into the first equation.

Front

What does the solution (3, 1) represent in the context of a system of equations?

Back

The solution (3, 1) represents the point where the two equations intersect, meaning x = 3 and y = 1 satisfy both equations.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What is the significance of the slopes of the lines in a system of equations?

Back

The slopes determine the relationship between the lines: parallel lines have no solution, intersecting lines have one solution, and coincident lines have infinitely many solutions.

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.

Front

What is the substitution method used for?

Back

The substitution method is used to solve systems of equations, particularly when one equation can be easily solved for one variable.