Mathematics
Grade 8
15 min
Solve a system of equations by graphing
Solve a system of equations by graphing
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a system of linear equations and its solution.
Graph a linear equation using the slope-intercept form.
Graph two linear equations on the same coordinate plane.
Identify the point of intersection of two graphed lines.
Determine if a point is a solution to a system of equations by substituting its coordinates.
Solve a system of two linear equations by graphing and verifying the solution.
Ever wondered how two different paths cross? 🗺️ Just like paths, two equations can 'cross' at a specific point, and we're going to find out where!
In this lesson, you'll learn how to solve a system of two linear equations by graphing them on a coordinate plane. This skill is crucial for understanding how different relationships can interact and f...
2
Key Concepts & Vocabulary
TermDefinitionExample
System of Linear EquationsA set of two or more linear equations that use the same variables.$\{ \begin{array}{l} y = 2x + 1 \\ y = -x + 4 \end{array}$
Linear EquationAn equation whose graph is a straight line. It can be written in the form $y = mx + b$ or $Ax + By = C$.$y = 3x - 5$
Solution to a SystemThe point (x, y) that makes ALL equations in the system true. Graphically, it's the point where the lines intersect.For the system $\{ \begin{array}{l} y = x + 1 \\ y = -x + 3 \end{array}$, the solution is $(1, 2)$ because $2 = 1 + 1$ and $2 = -1 + 3$ are both true.
Intersection PointThe single point where two or more lines cross each other on a graph. This point represents the solution to a system of equations.If line A crosses line B at $(3, 2)$, then $(3, 2)$ is...
3
Core Formulas
Slope-Intercept Form
$y = mx + b$
This is the most common form for graphing linear equations. 'm' represents the slope, and 'b' represents the y-intercept. You start by plotting the y-intercept $(0, b)$, then use the slope 'm' (rise/run) to find other points.
Standard Form of a Linear Equation
$Ax + By = C$
Sometimes equations are given in this form. To graph them easily using slope-intercept, you need to rearrange the equation to solve for 'y'. For example, $2x + y = 5$ becomes $y = -2x + 5$.
Identifying the Solution by Graphing
The solution to a system of two linear equations is the point $(x, y)$ where their graphs intersect.
After graphing both lines on the same coordinate plane, visually locate the point where they cross....
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
A system of two linear equations has a solution at (3, -2). The first equation is y = -2x + 4. The y-intercept of the second line is 1. What is the equation of the second line?
A.y = x + 1
B.y = -x + 1
C.y = -2x + 1
D.y = 3x + 1
Challenging
Two lines, Line A given by y = ax + 4 and Line B given by y = bx - 2, intersect at the point (2, 0). What is the correct system of equations?
A.{y = 2x + 4, y = -x - 2}
B.{y = -x + 4, y = 2x - 2}
C.{y = x + 4, y = -2x - 2}
D.{y = -2x + 4, y = x - 2}
Challenging
A student solves the system {y = (1/3)x + 2, y = -2x + 9}. They get an answer of (3, 4). The tutorial stresses the importance of checking solutions. Why is (3, 4) incorrect and what is the actual solution?
A.It's incorrect because it fails the first equation; the correct solution is (3, 3).
B.It's incorrect because it fails the second equation; the correct solution is (3, 3).
C.It's incorrect because the student forgot to convert to slope-intercept form; the correct solution is (4, 3).
D.It's incorrect because the student graphed the slopes incorrectly; the correct solution is (2, 5).
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free