Systems of Equations: Substitution Method

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 for two equations to intersect on a graph?

Back

It means that the solution (x, y) is the point where the two equations have the same values.

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

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

Back

You can substitute a value for x to find the corresponding value of y.

Front

What is the solution to the system of equations x = 6 and y = 2x - 3?

Back

(6, 9)

Front

How do you check if (x, y) is a solution to a system of equations?

Back

Substitute x and y into both equations to see if they hold true.

Front

What is the first step in using the substitution method?

Back

Solve one of the equations for one variable.

Front

What is the solution to the system of equations x = -3y - 17 and 2x + 3y = -7?

Back

(10, -9)

Front

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

Back

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

Front

What is the solution to the system of equations y = 3x + 14 and y = -4x?

Back

(-2, 8)