Solving Systems of Equations by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

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

Back

It involves 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

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the substitution method?

Back

A method for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

Given the equations 4x + 2y = 12 and y = 3x - 14, find the solution using substitution.

Back

(4, -2)

Front

Given the equations y = 5x + 7 and 8x - 8y = -24, find the solution using substitution.

Back

(4, -4)

Front

Given the equations y = -4x + 17 and y = -5x + 23, find the solution using substitution.

Back

(6, -7)

Front

Given the equations y = 8x + 9 and 2x + 6y = 8, find the solution using substitution.

Back

(-1, 1)

Front

Given the equations y = -6x - 2 and y = 4x - 12, find the solution using substitution.

Back

(1, -8)

Front

What is an infinite solution in a system of equations?

Back

When two equations represent the same line, resulting in an infinite number of solutions.