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Simultaneous Linear Equations

Answer Keys Here

Aligned To Common Core Standard:

Grade 8 Number System - 8.EE.C.7b

What are Simultaneous Linear Equations? Linear equations, a relatively newer concept for you as you get into grade 7, is a significant tool required to use in everyday applications. These equations are very helpful in describing a relationship between two variables in the physical world. They allow scientists to make predictions and conversions and calculate rates. Graphing linear equations make the trends visible. For example: y = 2x + 1 This is a linear equation. Two linear equations having two variables (x and y) taken together to solve are called simultaneous linear equations. Example of such two equations is: 2x - 3y = 4 3x + y = 1 The solution a simultaneous equation is presented in the form of an ordered pair (x, y). The steps to solve simultaneous linear equations are as follows: Equation 1: 2x + 3y = 8, Equation 2: 3x + 2y = 7 Step # 1: Multiply each equation with a number that makes the leading co-efficient the same. Step # 2: Find the difference between the two-equations. Subtract second from the first. Step # 3: Now solve the new equation that has only one variable. Step # 4: Substitute the value of this variable in either of the equations and find the other. Step # 5: Write the answer in an ordered pair.

Printable Worksheets And Lessons

Homework Sheets

I start this skill in a very basic manner. A flat line is always a good place to start.

  • Homework 1 - Solve this system of equations by graphing. Graph the equations, and then write the solution.
  • Homework 2 - Calculate the solution by graphing.
  • Homework 3 - This equation tells you that every y-value is 8. Plot some points that have a y value of 8, like (0, 8) and (1, 8), and then draw a line connecting them.

Practice Worksheets

"Solving systems" always makes it sound a lot more complicated than the topic really is.

  • Practice 1 - See where they all meet up?
  • Practice 2 - Take it all home for you.
  • Practice 3 - Make the Ys equal to each other and get this one going.

Math Skill Quizzes

For the answers, I tried to give you a snapshot of where the graph intersection is found.

  • Quiz 1 - Number three and four are a cinch.
  • Quiz 2 - Don't let the fractions through.
  • Quiz 3 - How much does the line rise and run?