Solving Systems of Equations

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?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

How do you determine if a system of equations has infinitely many solutions?

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If the equations represent the same line, every point on the line is a solution.

Front

What is the y-coordinate of the solution to the system x - 2y = 1 and x + 4y = 7?

Back

1

Front

How many horses and chickens are in a pasture if there are 28 animals and 80 legs?

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12 horses and 16 chickens.

Front

What system of equations represents Christian's brochure costs?

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4x + 3y = 134 and 3x + 3y = 120.