Mathematics
Grade 10
15 min
Solve a system of equations by graphing word problems
Solve a system of equations by graphing word problems
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate a real-world scenario into a system of two linear equations.
Define variables to represent unknown quantities in a word problem.
Write two linear equations in slope-intercept form (y = mx + b) that model a given situation.
Accurately graph two linear equations on the same coordinate plane.
Identify the point of intersection of two graphed lines as the solution to the system.
Interpret the meaning of the point of intersection in the context of the original word problem.
Verify the solution by substituting the coordinates into both original equations.
🚗 Planning a road trip and can't decide which car rental company is cheaper? Graphing two options can show you the exact mileage where the costs are equal!
This tutorial will teach you how t...
2
Key Concepts & Vocabulary
TermDefinitionExample
System of Linear EquationsTwo or more linear equations that share the same variables. The goal is to find the single ordered pair (x, y) that satisfies all equations simultaneously.y = 2x + 3 and y = -x + 9 form a system of linear equations.
Solution to a SystemThe ordered pair (x, y) where the graphs of the lines intersect. This point makes both equations in the system true.For the system y = x + 1 and y = 2x - 1, the solution is (2, 3) because the lines cross at that point.
Slope-Intercept FormA way of writing a linear equation, y = mx + b, which clearly shows the line's key properties.In the equation y = 4x + 5, the slope 'm' is 4 and the y-intercept 'b' is 5.
Y-Intercept (b)The point where the line crosses the vertical y-axis. In word pro...
3
Core Formulas
Defining Variables
Let x = [independent quantity] and Let y = [dependent quantity]
Before writing equations, you must define what your variables represent. The independent variable (x) is what you control (e.g., number of months, items sold), and the dependent variable (y) is the outcome (e.g., total cost, total revenue).
Slope-Intercept Form
y = mx + b
Use this formula to structure your equations. Identify the rate of change in the word problem for 'm' (the slope) and the initial or fixed value for 'b' (the y-intercept).
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Two trains are traveling on parallel tracks. Train A starts at mile marker 10 and travels at 60 mph. Train B starts at mile marker 0 and travels at 75 mph. When will Train B catch up to Train A?
A.After 30 minutes.
B.After 40 minutes.
C.After 50 minutes.
D.After 1 hour.
Challenging
A family is choosing a venue for a party. Venue A: $200 fee, $10/person. Venue B: $50 fee, $15/person. Venue C: $500 flat fee for up to 50 people. When is Venue B the cheapest option?
A.For fewer than 30 guests.
B.For between 30 and 43 guests.
C.For more than 43 guests.
D.Venue B is never the cheapest option.
Challenging
A student analyzes the 'Two Job Offers' problem (Company A: y=0.10x+200, Company B: y=0.05x+350). They graph the lines and find the intersection at (3000, 500). The student concludes: 'To earn exactly $3000, you must make $500 in sales.' What is the fundamental error in this interpretation?
A.The student calculated the intersection point incorrectly.
B.The student correctly identified the values but did not answer the full question.
C.The student swapped the meanings of the x and y variables.
D.The student should have used substitution instead of graphing.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free