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 equations.

Front

How do you solve a 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.

Front

What is the solution of a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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 infinite solutions?

Back

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

Front

Given the equations y = -2 and 4x - 3y = 18, find the solution.

Back

(3, -2)

Front

Given the equations 2x - 3y = -1 and y = x - 1, find the solution.

Back

(4, 3)

Front

Solve the system: y = 8x + 1 and y = 6x + 3.

Back

(1, 9)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves plotted on a coordinate plane.