System of Equations Substitution.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does substitution mean in the context of solving equations?

Back

Substitution is the process of replacing a variable with an equivalent expression to solve an equation.

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the first step in solving the system of equations: 2x + 3y = 6 and y = x - 2?

Back

Substitute y = x - 2 into the first equation.

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how do you start solving by substitution?

Back

Substitute y = 2x + 3 into the second equation.

Front

What is the solution to the system of equations: x + y = 10 and y = 2x?

Back

(2, 8) after substituting y = 2x into the first equation.

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

Back

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

Front

How can you check your solution for a system of equations?

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.