Mathematics
Grade 10
15 min
Solve a system of equations by graphing
Solve a system of equations by graphing
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1
Introduction & Learning Objectives
Learning Objectives
Graph a linear equation from slope-intercept form (y = mx + b).
Graph a linear equation from standard form (Ax + By = C) by finding intercepts.
Identify the point of intersection of two graphed lines as the solution to the system.
Classify a system of equations as having one solution, no solution, or infinitely many solutions based on its graph.
Verify the solution to a system of equations by substituting the coordinates into the original equations.
Interpret the solution of a system of equations in the context of a real-world problem.
Imagine two friends are running towards each other from different starting points. How can you find the exact time and place they will meet? 🏃♀️🤝🏃♂️ Graphing can show you!
This tutorial will teach you a visual method...
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Key Concepts & Vocabulary
TermDefinitionExample
System of Linear EquationsA set of two or more linear equations that share the same variables.y = 2x + 1 and y = -x + 7 form a system of equations. The variables are x and y.
Solution to a SystemAn ordered pair (x, y) that makes all equations in the system true. On a graph, this is the point where the lines intersect.For the system y = x + 2 and y = -x + 4, the ordered pair (1, 3) is the solution because 3 = 1 + 2 and 3 = -1 + 4 are both true statements.
Point of IntersectionThe specific point on a coordinate plane where two or more lines cross each other. The coordinates of this point are the solution to the system.If two lines cross at the point (4, -2), then the solution to the system is x=4 and y=-2.
Consistent SystemA system of equations that has at least one so...
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Core Formulas
Slope-Intercept Form
y = mx + b
This is the most common form for graphing. 'b' is the y-intercept, which is your starting point on the y-axis. 'm' is the slope, which tells you the 'rise over run' (how many units to move up/down and right/left) to find the next point.
Standard Form
Ax + By = C
This form is useful for finding the x- and y-intercepts. To find the y-intercept, set x=0 and solve for y. To find the x-intercept, set y=0 and solve for x. Plot these two points and draw a straight line through them.
5 more steps in this tutorial
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Challenging
What is the solution to the system of equations graphed by the lines y = 3 and 4x - 2y = 4?
A.(4, 3)
B.(3, 4)
C.(1, 3)
D.(2.5, 3)
Challenging
For the system Ax + By = C and Dx + Ey = F to be inconsistent, which condition must be met (assuming B, E ≠ 0)?
A.-A/B = -D/E and C/B ≠ F/E
B.-A/B = -D/E and C/B = F/E
C.A/B = D/E and C/B = F/E
D.-A/B ≠ -D/E
Challenging
Two friends, Sarah and Tom, are saving for a concert. Sarah starts with $10 and saves $15 per week. Tom starts with $25 and saves $10 per week. A system of equations is created to model their savings. When graphed, what will the solution represent?
A.The total amount they save together.
B.The week when they both have the same amount of money.
C.The difference in their starting amounts.
D.The number of weeks it takes Sarah to save more than Tom.
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