Writing Systems of Equations

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 set of values that satisfy all equations in the system.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common.

Front

What does it mean for two equations to be independent?

Back

Two equations are independent if they have exactly one solution, meaning they intersect at a single point.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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

How do you solve a system of equations by elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

Front

What is the graphical method of solving a system of equations?

Back

Graph both equations on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

Front

What is the importance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting the number and type of solutions.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.