Chapter 5: Q 96. (page 611)

Solve the system of equation $\{\begin{cases} - x - 12 y = - 1 \\ 2 x - 8 y = - 6 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(- 2, 0.25)$ .

Step by step solution

Step 1. Given information

The given equations are:

$- x - 12 y = - 1 \dots \dots (1)$

$2 x - 8 y = - 6 \dots \dots (2)$

Step 2. Substitute value of x from equation 1 in equation 2

From equation $(1)$ $x = 1 - 12 y$

Substitute in equation $(2)$

localid="1649347861698" $\Rightarrow 2 (1 - 12 y) - 8 y = - 6$

Step 3. Solve for y

$\Rightarrow 2 - 24 y - 8 y = - 6$

$\Rightarrow - 32 y = - 8$

$\Rightarrow y = \frac{8}{32}$

$\Rightarrow 0.25$

Step 4. Substitute value of y from step 3 in equation 1

$\Rightarrow - x - 12 (0.25) = - 1$

$\Rightarrow - x - 3 = - 1$

$\Rightarrow x = 1 - 3$

$\Rightarrow x = - 2$

Step 5. Checking solution

As we know $x = - 2$ and $y = 0.25$

Put these values in equation $(1)$

localid="1649348056337" $\Rightarrow - (- 2) - 12 (0.25) = - 1$

$\Rightarrow - 1 = - 1$

Als put these values in equation $(2)$

localid="1649348080137" $\Rightarrow 2 (- 2) - 8 (0.25) = - 6$

localid="1649348095034" $\Rightarrow - 6 = - 6$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve the system of equation $\{\begin{cases} - x - 12 y = - 1 \\ 2 x - 8 y = - 6 \end{cases}$ by substitution

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute value of x from equation 1 in equation 2

Step 3. Solve for y

Step 4. Substitute value of y from step 3 in equation 1

Step 5. Checking solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the system of equation-x-12y=-12x-8y=-6by substitution

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute value of x from equation 1 in equation 2

Step 3. Solve for y

Step 4. Substitute value of y from step 3 in equation 1

Step 5. Checking solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the system of equation $\{\begin{cases} - x - 12 y = - 1 \\ 2 x - 8 y = - 6 \end{cases}$ by substitution