Solving Systems of Equations - algebra 1

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 it mean to solve a system of equations by elimination?

Back

It involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other variable.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

Identify variables for the unknowns, translate the relationships and conditions into equations.

Front

What is the graphical interpretation of a system of equations?

Back

The solutions are the points where the graphs of the equations intersect.

Front

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

Back

They represent the rate of change or the relationship between the variables in the equations.

Front

How can you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.

Front

What is the meaning of dependent and independent systems of equations?

Back

Dependent systems have infinitely many solutions (the same line), while independent systems have exactly one solution (intersecting lines).

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.