Solving Systems of Equations 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 by itself.

Front

What is the first step in solving the system y = 2x + 0 and y = 6 - x by substitution?

Back

The first step is to set the two equations equal to each other since they both equal y: 2x = 6 - x.

Front

What is the solution to the system y = 2x + 0 and y = 6 - x?

Back

The solution is (-1, 7).

Front

What is the solution to the system y = -3x + 2 and y = 3x - 4?

Back

The solution is (1, -1).

Front

What is the solution to the system y = x + 17 and y = 4x + 2?

Back

The solution is (5, 22).

Front

What is the solution to the system y = -x + 27 and y = x + 3?

Back

The solution is (12, 15).

Front

What is the solution to the system y = 2x + 10 and y = x + 7?

Back

The solution is (-3, 4).

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.