Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Multiply the 2nd equation by -4. What value belongs in the green box?

[tex]\[
\begin{array}{rr}
-2x + 4y = 15 \\
3x + y = 2 \\
(3x + y = 2) \xrightarrow{\text{multiply by } -4}
\end{array}
\][/tex]

[tex]\[
\begin{array}{rr}
-2x + 4y = 15 \\
-12x - 4y = -8
\end{array}
\][/tex]

What value belongs in the green box?

A. [tex]\(12x\)[/tex]
B. [tex]\(3x\)[/tex]
C. [tex]\(-12x\)[/tex]
D. [tex]\(-x\)[/tex]

Sagot :

GinnyAnswer
Sure, let's solve the problem step by step.

We are given two equations:
1. [tex]\(-2x + 4y = 15\)[/tex],
2. [tex]\(3x + y = 2\)[/tex].

The problem asks us to multiply the second equation by [tex]\(-4\)[/tex] and determine the coefficient that would appear in place of [tex]\(3x\)[/tex] when multiplied by [tex]\(-4\)[/tex] and placed in the corresponding position in the new equation.

Let's start by writing the second equation:
[tex]\[ 3x + y = 2 \][/tex]

Step-by-step multiplication by [tex]\(-4\)[/tex]:

1. Multiply the [tex]\(3x\)[/tex] term by [tex]\(-4\)[/tex]:
[tex]\[ -4 \cdot 3x = -12x \][/tex]

2. Multiply the [tex]\(y\)[/tex] term by [tex]\(-4\)[/tex]:
[tex]\[ -4 \cdot y = -4y \][/tex]

3. Multiply the constant term [tex]\(2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ -4 \cdot 2 = -8 \][/tex]

Thus, after multiplying the second equation [tex]\(3x + y = 2\)[/tex] by [tex]\(-4\)[/tex], the new equation will be:
[tex]\[ -12x - 4y = -8 \][/tex]

The value that belongs in the green box is the coefficient of the [tex]\(x\)[/tex] term in this new equation, which is [tex]\(\boxed{-12}\)[/tex].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.