Twin-Quill ScribeTwin-Links · systems of equations

Writes two equations at once: turning a story into a system.

Systems of Equations Word Problems

Turning a story into a system. In MathBound, the free Algebra I adventure game, Twin-Quill Scribe 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

Translate to a System. Translate a direct relationship word problem into a system of two equations.
Number Problems. Solve a basic number problem involving sum and difference.
Geometry Applications. Solve for complementary or supplementary angles using a system of equations.

Worked examples

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

Example 1 · Translate to a System

The

sum

of

two

numbers

is

12,

and

the

larger

is

3

times

the

smaller.

Let

x

be

the

larger

and

y

the

smaller.

Which

system

models

this?

$3 x + y = 12$ $and$ $x = 3 y$
$x + y = 12$ $and$ $y = 3 x$
$x + y = 12$ $and$ $x = y + 3$
$x + y = 12$ $and$ $x = 3 y$

Show the worked steps

$" The$ $sum$ $is$ $12"$ $gives$ $x + y = 12 .$
$" The$ $larger$ $is$ $3$ $times$ $the$ $smaller "$ $gives$ $x = 3 y .$

Answer: $x + y = 12$ $and$ $x = 3 y$

Example 2 · Number Problems

The

sum

of

two

numbers

is

72

and

their

difference

is

12 .

What

is

the

larger

number?

$36$
$42$
$30$
$60$

Show the worked steps

$Adding$ $x + y = 72$ $and$ $x - y = 12 : 2 x = 84 .$
$So$ $the$ $larger$ $is$ $42 .$

Answer: $42$

Example 3 · Geometry Applications

Two

angles

are

complementary.

The

larger

is

3 6^{\circ}

more

than

twice

the

smaller.

Find

both

angles.

$7 0^{\circ}$ $and$ $1 9^{\circ}$
$3 6^{\circ}$ $and$ $5 4^{\circ}$
$7 2^{\circ}$ $and$ $1 8^{\circ}$
$7 4^{\circ}$ $and$ $1 7^{\circ}$

Show the worked steps

$x + y = 90$ $and$ $x = 2 y + 36 .$
$3 y + 36 = 90,$ $so$ $y = 1 8^{\circ}$ $and$ $x = 7 2^{\circ} .$

Answer: $7 2^{\circ}$ $and$ $1 8^{\circ}$

Where it is in your textbook

Textbook	Lessons
Standard course	6.4
Big Ideas Math Algebra 1	5.2
Big Ideas Math Algebra 1 (2022)	5.2
Carnegie Learning Algebra I	M2 3.1, M2 3.5
CPM Core Connections Algebra	4.1.2, 4.3.1
CPS Skyline Algebra	5.8-5.9
enVision Algebra 1	4-2
enVision Algebra 1 (2024)	4-2
Eureka Math Algebra I (EngageNY)	1.24
Glencoe Algebra 1	6-5
HMH Into Algebra 1	9.2, 9.4
Holt McDougal Larson Algebra 1	6.2, 6.3
Illustrative Mathematics Algebra 1	2.12
Illustrative Mathematics Algebra 1 (v.360)	2.12, 2.18-2.19
Math Nation Algebra 1 (Florida B.E.S.T.)	5.8, 5.11
MVP Mathematics I (Integrated Math 1)	5.1, 5.8
Open Up NC Math 1 (MVP)	5.1, 5.8
OpenStax Elementary Algebra 2e	5.4
Pearson Algebra 1 Common Core	6-4
Reveal Algebra 1	7-2, 7-4
SpringBoard Algebra 1	17

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