Cancel CrabTwin-Links · systems of equations

Two matching claws that clap and cancel: solving systems by elimination.

Solving Systems by Elimination

Solving systems by elimination. In MathBound, the free Algebra I adventure game, Cancel Crab 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.

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

What you will practice

Elimination Method. Solve a system where one variable eliminates when the equations are directly added.
Classify Systems Algebraically. Identify an inconsistent system using elimination (results in a false statement indicating no solution).
Choose Most Convenient Method. Determine whether substitution or elimination is more efficient based on the equations' initial forms.

Worked examples

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

Example 1 · Elimination Method

At

a

fair,

5

hot

dogs

and

1

drink

cost

$13,

and

5

hot

dogs

and

5

drinks

cost

$25 .

What

does

one

drink

cost,

in

dollars?

$3$
$6.33$
$12$
$2$

Show the worked steps

$With$ $x$ $for$ $a$ $hot$ $dog$ $and$ $y$ $for$ $a$ $drink:$ $5 x + y = 13$ $and$ $5 x + 5 y = 25 .$ $The$ $hot$ $dogs$ $match.$
$Subtract:$ $4 y = 12,$ $so$ $y = 3 .$

Answer: $3$

Example 2 · Classify Systems Algebraically

Solving

which

system

by

elimination

produces

a

false

statement,

so

it

has

no

solution?

$- 4 x - 2 y = - 8$ $and$ $8 x + 4 y = 16$
$- 3 x - 4 y = 9$ $and$ $6 x + 8 y = - 15$
$4 x + 2 y = 2$ $and$ $8 x + 4 y = 4$
$- 5 x - 5 y = 15$ $and$ $- 5 x + 5 y = 5$

Show the worked steps

$One$ $equation$ $is$ $a$ $multiple$ $of$ $the$ $other$ $on$ $the$ $left$ $but$ $not$ $the$ $right,$ $so$ $the$ $variables$ $cancel$ $and$ $leave$ $something$ $false.$

Answer: $- 3 x - 4 y = 9$ $and$ $6 x + 8 y = - 15$

Example 3 · Choose Most Convenient Method

Which

method

is

more

efficient

for

2 x + 2 y = - 10

and

4 x - 2 y = 5 ?

$Elimination,$ $because$ $subtracting$ $the$ $equations$ $cancels$ $a$ $variable$ $straight$ $away$
$Substitution,$ $because$ $one$ $equation$ $is$ $already$ $solved$ $for$ $x$
$Substitution,$ $because$ $one$ $equation$ $is$ $already$ $solved$ $for$ $y$
$Elimination,$ $because$ $adding$ $the$ $equations$ $cancels$ $a$ $variable$ $straight$ $away$

Show the worked steps

$Opposite$ $coefficients$ $mean$ $adding$ $the$ $equations$ $removes$ $a$ $variable$ $with$ $no$ $scaling.$

Answer: $Elimination,$ $because$ $adding$ $the$ $equations$ $cancels$ $a$ $variable$ $straight$ $away$

Where it is in your textbook

Textbook	Lessons
Standard course	6.3
Big Ideas Math Algebra 1	5.3, 5.4
Big Ideas Math Algebra 1 (2022)	5.3, 5.4
Carnegie Learning Algebra I	M2 3.2, M2 3.5
CPM Core Connections Algebra	4.2.3, 4.2.4, 4.2.5
CPS Skyline Algebra	5.8-5.9, 5.10, 5.11H-5.12H
enVision Algebra 1	4-3
enVision Algebra 1 (2024)	4-3
Eureka Math Algebra I (EngageNY)	1.22-1.23
Glencoe Algebra 1	6-3, 6-4, 6-5
HMH Into Algebra 1	9.3, 9.4
Holt McDougal Larson Algebra 1	6.3, 6.4, 6.5
Illustrative Mathematics Algebra 1	2.14-2.16, 2.17
Illustrative Mathematics Algebra 1 (v.360)	2.14-2.16, 2.17
Math Nation Algebra 1 (Florida B.E.S.T.)	5.9, 5.10, 5.11
MVP Mathematics I (Integrated Math 1)	5.8, 5.9, 5.10, 8.9, 8.10
Open Up NC Math 1 (MVP)	5.8, 5.9, 5.10
OpenStax Elementary Algebra 2e	5.3
Pearson Algebra 1 Common Core	6-3, 6-4
Reveal Algebra 1	7-3, 7-4
SpringBoard Algebra 1	17

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