Solve a system of equations using substitution: word problems

Learning Objectives Identify two unknown quantities in a word problem. Represent unknown quantities with variables and form two simple equations from a word problem. Express one variable in terms of another from one of the equations. Substitute an algebraic expression for a variable into the second equation. Solve the resulting single-variable equation using multiplication and other operations. Calculate the value of the second unknown quantity. Verify the solution by checking it against the original word problem. Ever wonder how detectives solve mysteries with two clues? 🕵️‍♀️ In math, we can be detectives too, using two clues (equations) to find two secret numbers! In this lesson, you'll learn how to solve word problems that have two unknown numbers. We'll use...

TermDefinitionExample VariableA letter (like 'x' or 'y') that stands for an unknown number in a mathematical problem.In the problem 'x + 5 = 12', 'x' is the variable representing the unknown number. EquationA mathematical sentence that shows two expressions are equal. It always has an equals sign (=).2y + 3 = 11 is an equation. It states that '2y + 3' has the same value as '11'. System of EquationsTwo or more equations that share the same unknown variables. We're looking for values that make ALL equations true at the same time.x = y + 5 and x + y = 15 form a system of equations because they both use 'x' and 'y'. SubstitutionThe act of replacing a variable in an equation with an equivalent expression or va...

Identify Unknowns and Assign Variables Let [variable 1] = [first unknown quantity], Let [variable 2] = [second unknown quantity] Read the word problem carefully to find the two quantities you need to figure out. Assign a different letter (variable) to each one. This helps organize your thoughts. Formulate Two Equations Translate the problem's sentences into two mathematical equations using your variables. For example, 'one number is 3 more than another' becomes `x = y + 3`. Each piece of information in the word problem usually gives you a clue to write an equation. Look for keywords like 'is', 'total', 'sum', 'difference', 'twice', 'half'. The Substitution Principle If `A = B` and you have anoth...