Solving Systems of Equations by Substitution Method

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

Rearranging the equation to get the variable on one side and the constants on the other.

Front

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

Back

Solve one of the equations for one variable in terms of the other variable.

Front

If x = 3y, what is y in terms of x?

Back

y = x/3.

Front

What is the solution to the system: 2y + x = -15 and x = 3y?

Back

(-9, -3).

Front

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

Back

Substitute the solution back into both equations to see if they hold true.

Front

What is the significance of a unique solution in a system of equations?

Back

It means there is exactly one set of values for the variables that satisfies all equations.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect.