Searchlight ScoutTwin-Links · systems of equations

Two searchlight beams that cross at one point: solving systems by graphing.

Solving Systems by Graphing

Solving systems by graphing. In MathBound, the free Algebra I adventure game, Searchlight Scout asks these problems, and the only way past is to solve them.

Part of Systems of Equations and Inequalities: chapter 6 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Verify Solutions.
Solve by Graphing. Solve a system by graphing when both equations are given in slope-intercept form.
Classify Systems. Identify a system with exactly one solution (consistent and independent).

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Verify Solutions

(1, 2)

solves

the

system

- 2 x + 5 y = □

and

- x + 2 y = 3 .

What

number

goes

in

the

box?

$- 12$
$8$
$1$
$3$

Show the worked steps

$Substitute$ $x = 1$ $and$ $y = 2$ $into$ $the$ $left$ $side.$
$- 2 (1) + 5 (2) = 8 .$

Answer: $8$

Example 2 · Solve by Graphing

At

what

value

of

x

do

the

lines

y = 3 x - 5

and

y = x + 3

cross?

$7$
$- 5$
$- 4$
$4$

Show the worked steps

$Set$ $the$ $right$ $sides$ $equal:$ $3 x - 5 = x + 3 .$
$2 x = 8,$ $so$ $x = 4 .$

Answer: $4$

Example 3 · Classify Systems

How

many

solutions

does

the

system

2 x + 2 y = 10

and

2 x - 5 y = 3

have?

$No$ $solution$
$Exactly$ $two$ $solutions$
$Exactly$ $one$ $solution$
$Infinitely$ $many$ $solutions$

Show the worked steps

$Different$ $slopes$ $mean$ $the$ $lines$ $cross$ $exactly$ $once.$
$So$ $it$ $has$ $exactly$ $one$ $solution .$

Answer: $Exactly$ $one$ $solution$

Where it is in your textbook

Textbook	Lessons
Standard course	6.1, 6.6
Big Ideas Math Algebra 1	5.1, 5.4, 5.5, 5.7
Big Ideas Math Algebra 1 (2022)	5.1, 5.4, 5.5, 5.7
Carnegie Learning Algebra I	M2 3.1, M2 3.4
CPM Core Connections Algebra	4.2.1, 4.2.2, 9.4.1, 9.4.2
CPS Skyline Algebra	3.6, 5.5-5.6, 5.7, 5.10
enVision Algebra 1	4-1, 4-5
enVision Algebra 1 (2024)	4-1, 4-5
Eureka Math Algebra I (EngageNY)	1.22-1.23
Glencoe Algebra 1	6-1, 6-6
HMH Into Algebra 1	9.1, 10.2
Holt McDougal Larson Algebra 1	3.5 Ext, 6.1, 6.5, 6.6
Illustrative Mathematics Algebra 1	2.12, 2.17, 2.24-2.26
Illustrative Mathematics Algebra 1 (v.360)	2.12, 2.17, 4.7-4.9
Math Nation Algebra 1 (Florida B.E.S.T.)	5.6, 5.7, 6.9, 6.10
MVP Mathematics I (Integrated Math 1)	5.1, 5.6, 5.7, 5.10
Open Up NC Math 1 (MVP)	5.1, 5.6, 5.7, 5.10
OpenStax Elementary Algebra 2e	5.1, 5.6
Pearson Algebra 1 Common Core	6-1, 6-6
Reveal Algebra 1	7-1, 7-5
SpringBoard Algebra 1	17, 18

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