Solving Systems of Equations by Substitution

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

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the first step in solving the system: y = 3x - 8 and y = 4 - x?

Back

Substitute the expression for y from one equation into the other equation.

Front

What is the solution to the system: y = 3x - 8 and y = 4 - x?

Back

The solution is (3, 1).

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.

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

Back

If two lines are parallel, the system has no solution because the lines never intersect.

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What is the solution to the system: y = 4x + 6 and -5x - y = 21?

Back

The solution is (-3, -6).

Front

What is the solution to the system: y = 6x - 11 and -2x - 3y = -7?

Back

The solution is (2, 1).