Lesson 13 (1 & 2) 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 substitution method?

Back

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

Front

Solve the system: 2y + x = -15, x = 3y

Back

(-9, -3)

Front

Solve the system: y = 2x + 1, y = 4x - 1

Back

(1, 3)

Front

What is an infinite solution in a system of equations?

Back

An infinite solution occurs when the equations represent the same line, meaning there are countless points of intersection.

Front

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

Back

No solution means the lines represented by the equations are parallel and never intersect.

Front

Solve the system: y = 8x + 1, y = 6x + 3

Back

(1, 9)

Front

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

Back

Identify one equation to solve for one variable.