How Do You Solve a Word Problem Using Two Equations?

How Do You Solve a Word Problem Using Two Equations?

Note:

Sometimes word problems describe a system of equations, two equations each with two unknowns. Solving word problems like this one aren't so bad if you know what to do. Check it out with this tutorial!

Keywords:

  • problem
  • word problem
  • translate words to algebra
  • translate
  • linear equation
  • system of linear equations
  • 2 equations 2 unknowns
  • solve by substitution
  • substitution
  • solve by division
  • apply distributive property
  • simplify
  • expression
  • equation
  • check
  • evaluate

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

  • Apply the properties of operations to generate equivalent expressions.

  • Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

      • How Do You Solve Two Equations with Two Variables?How Do You Solve Two Equations with Two Variables?

      How Do You Solve Two Equations with Two Variables?

      Trying to solve two equations each with the same two unknown variables? Take one of the equations and solve it for one of the variables. Then plug that into the other equation and solve for the variable. Plug that value into either equation to get the value for the other variable. This tutorial will take you through this process of substitution step-by-step!

  • Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Further Exploration

  • Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

      • What's a System of Linear Equations?What's a System of Linear Equations?

      What's a System of Linear Equations?

      A system of equations is a set of equations with the same variables. If the equations are all linear, then you have a system of linear equations! To solve a system of equations, you need to figure out the variable values that solve all the equations involved. This tutorial will introduce you to these systems.