Solving Systems by Graphing and Substitution

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

How do you solve for y in the equation y + 2 = 3x?

Back

To solve for y, subtract 2 from both sides: y = 3x - 2.

Front

What does it mean for an ordered pair to be a solution to a system of equations?

Back

An ordered pair is a solution if it satisfies all equations in the system.

Front

What is the solution to the system of equations -x + 7y = 9 and -2x + 14y = 6?

Back

The ordered pair (0, 4) is NOT a solution to this system.

Front

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

Back

The solution is the ordered pair (0, 5).

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and substitute that expression into another equation.

Front

What does it mean for a solution to a system of equations to be 'true'?

Back

A solution is 'true' if it makes both equations in the system valid when substituted back into the equations.

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the ordered pair into both equations; if both equations are satisfied, it is a solution.

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.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied.