Solving Systems of Equations- Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does substitution mean in solving equations?

Back

Substitution is the process of replacing a variable in one equation with an equivalent expression from another equation.

Front

How do you solve for y in the equation y = 2x?

Back

To solve for y, substitute any value of x into the equation. For example, if x = 3, then y = 2(3) = 6.

Front

What is the first step in solving the system 5x - 2y = 3 and y = 2x using substitution?

Back

Substitute 2x for y in the first equation: 5x - 2(2x) = 3.

Front

What is the solution to the system 5x - 2y = 3 and y = 2x?

Back

The solution is (3, 6).

Front

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

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

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

Back

It means that the equations represent the same line, and there are countless points of intersection.

Front

How do you determine if a system of equations has one solution, no solution, or infinite solutions?

Back

Graph the equations; if they intersect at one point, there's one solution; if they are parallel, there's no solution; if they are the same line, there are infinite solutions.

Front

What is the solution to the system 2y + x = -15 and x = 3y?

Back

The solution is (-9, -3).

Front

What is the process to solve the system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.