Swap ShuttleTwin-Links · systems of equations

Swaps one part for its twin: solving systems by substitution.

Solving Systems by Substitution

Solving systems by substitution. In MathBound, the free Algebra I adventure game, Swap Shuttle 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

Substitution Method. Solve a system where one equation is already solved for x or y.
Classify Systems Algebraically. Identify an inconsistent system (results in a false statement indicating no solution).

Worked examples

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

Example 1 · Substitution Method

Solve

by

substitution : y = 2 x + 12

and

y = 4 x + 22

$- 5$
$(- 5, 2)$
$2$
$(2, - 5)$

Show the worked steps

$Both$ $equal$ $y,$ $so$ $2 x + 12 = 4 x + 22 .$
$x = - 5,$ $and$ $then$ $y = 2 .$

Answer: $(- 5, 2)$

Example 2 · Classify Systems Algebraically

What

do

the

graphs

of

the

equations

in

- 4 x + y = - 7

and

- 12 x + 3 y = - 18

look

like?

$The$ $same$ $line,$ $drawn$ $twice$
$Two$ $parallel$ $lines$ $that$ $never$ $meet$
$Two$ $lines$ $that$ $cross$ $at$ $one$ $point$
$Two$ $lines$ $that$ $cross$ $at$ $the$ $origin$

Show the worked steps

$The$ $left$ $sides$ $are$ $multiples$ $of$ $each$ $other$ $but$ $the$ $right$ $sides$ $are$ $not,$ $so$ $the$ $slopes$ $match$ $and$ $the$ $intercepts$ $differ.$
$So$ $the$ $graphs$ $are:$ $two$ $parallel$ $lines$ $that$ $never$ $meet.$

Answer: $Two$ $parallel$ $lines$ $that$ $never$ $meet$

Example 3 · Substitution Method

At

what

value

of

x

do

the

lines

y = x + 4

and

y = - 3 x + 16

cross?

$- 12$
$7$
$3$
$- 3$

Show the worked steps

$Both$ $are$ $y,$ $so$ $substitute$ $one$ $into$ $the$ $other:$ $x + 4 = - 3 x + 16 .$
$4 x = 12,$ $so$ $x = 3 .$

Answer: $3$

Where it is in your textbook

Textbook	Lessons
Standard course	6.2, 6.4
Big Ideas Math Algebra 1	5.2, 5.4
Big Ideas Math Algebra 1 (2022)	5.2, 5.4
Carnegie Learning Algebra I	M2 3.1, M2 3.5
CPM Core Connections Algebra	4.1.2, 4.2.1, 4.2.3, 4.2.5, 4.3.1, 10.3.1
CPS Skyline Algebra	5.7, 5.8-5.9, 5.10
enVision Algebra 1	4-2
enVision Algebra 1 (2024)	4-2
Eureka Math Algebra I (EngageNY)	1.22-1.23, 1.24
Glencoe Algebra 1	6-2, 6-3, 6-5
HMH Into Algebra 1	9.2, 9.3, 9.4
Holt McDougal Larson Algebra 1	6.2, 6.3, 6.5
Illustrative Mathematics Algebra 1	2.13, 2.17
Illustrative Mathematics Algebra 1 (v.360)	2.13, 2.17, 2.18-2.19
Math Nation Algebra 1 (Florida B.E.S.T.)	5.8, 5.10, 5.11
MVP Mathematics I (Integrated Math 1)	5.1, 5.10, 8.10
Open Up NC Math 1 (MVP)	5.1, 5.10
OpenStax Elementary Algebra 2e	5.2, 5.4
Pearson Algebra 1 Common Core	6-2, 6-4
Reveal Algebra 1	7-2, 7-3, 7-4
SpringBoard Algebra 1	17

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