Solving Systems of Equations Warm Up

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 substitution?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

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

Front

How do you graph a linear equation?

Back

You plot points that satisfy the equation and connect them to form a line.

Front

What is the solution to a system of equations?

Back

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

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

Back

It means there are infinitely many solutions, as the lines are the same.

Front

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

Back

Isolate one variable in one of the equations.

Front

What is the purpose of graphing a system of equations?

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To visually find the point of intersection, which represents the solution.

Front

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

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.