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 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

What is the first step in solving a system of equations by substitution?

Back

The first step is to isolate one variable in one of the equations.

Front

Given the equations y = 2x + 5 and -4x + y = 9, how do you solve for x?

Back

Substitute y from the first equation into the second: -4x + (2x + 5) = 9.

Front

What is the solution to the system 5x + y = -10 and y = -6x - 13?

Back

The solution is (-3, 5).

Front

What does it mean if a system of equations has no solution?

Back

It means 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

How can 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 graphical representation of a system of equations?

Back

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

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on the line is a solution.