➕ Algebra 1 · Systems of Equations
Solving Systems by Graphing flashcards
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All 16 flashcards at a glance
Card 1
What is a system of equations?
Two or more equations that use the same variables and must be true at the same time. In this lesson, two linear equations in x and y.
Card 2
What is the solution of a system of two linear equations?
The ordered pair (x, y) that makes both equations true. On the graph, it is the point where the two lines cross.
Card 3
Why is the point where two lines cross the solution of the system?
A point on the first line fits the first equation, and a point on the second line fits the second. A point on both lines fits both, which is exactly a solution of the system.
Card 4
What are the steps for solving a system by graphing?
Write each equation as y = mx + b. Graph both lines on the same axes. Read the crossing point. Check it in both equations. Write the pair (x, y).
Card 5
Is (−2, 7) a solution of y = −x + 5 and y = 2x + 11?
Yes. First: −(−2) + 5 = 7. Second: 2(−2) + 11 = 7. Both are true.
Card 6
Is (6, 1) a solution of x − y = 5 and x + y = 9?
No. 6 − 1 = 5 is true, but 6 + 1 = 7, not 9. It fits only the first equation.
Card 7
Two lines have the same slope and different y-intercepts. How many solutions does the system have?
None. The lines are parallel, so they never meet.
Card 8
Two lines have the same slope and the same y-intercept. How many solutions does the system have?
Infinitely many. They are the same line, so every point on it is a solution.
Card 9
Two non-vertical lines have slopes 4 and −1/2. How many solutions does the system have?
Exactly one. Different slopes mean the lines cross exactly once.
Card 10
Where do the lines x = −4 and y = 6 cross?
At (−4, 6). The vertical line has x-coordinate −4 everywhere, and the horizontal line has y-coordinate 6 everywhere.
Card 11
Rewrite 4x + y = 7 in slope-intercept form so you can graph it.
Subtract 4x from both sides: y = −4x + 7. So b = 7 and the slope is −4.
Card 12
You read a crossing point from a graph as (5, 4). What should you do before you call it the solution?
Check it in both original equations. If either is false, the point is not the solution.
Card 13
The lines cross between grid lines. Can you read an exact solution from the graph?
No. You can only estimate it, such as “about (4.6, 2.2).” Check the estimate, and use algebra for the exact answer.
Card 14
A student writes the solution as “x = 3.” Why is that incomplete?
A solution of a system in x and y is an ordered pair. It needs both numbers, like (3, y) with the y-value filled in.
Card 15
How is the crossing of y = 2x + 9 and y = 5x connected to the equation 2x + 9 = 5x?
At the crossing the two y-values are equal, so the x-coordinate of the crossing solves that equation. Here 9 = 3x, so x = 3, and y = 15.
Card 16
In this lesson’s GRID memory trick, what do the letters stand for?
Get each equation ready to graph, Ruler-draw both lines on one grid, Identify the crossing point, Double-check in both equations.