Solving Systems of Equations by Substitution and Elimination

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 point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What does it mean to solve a system of equations by elimination?

Back

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

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations. If both equations are true, the solution is correct.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

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

Back

Isolate one variable in one of the equations.

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

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Align the equations and manipulate them (if necessary) to have the same coefficient for one of the variables.

Front

What is the solution to the system: y = 2x - 6 and y = -5x + 15?

Back

(3, 0)

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What is the solution to the system: 4x + 2y = 12 and y = 3x - 14?

Back

(4, -2)

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What is the solution to the system: 8x - 6y = 0 and y = 3x + 5?

Back

(-3, -4)