Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

(iii)
Solve the following system of equations:
[tex]\[
\begin{array}{l}
5x - 7y - 21 = 0 \\
25x - 35y = 63
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To solve the given system of equations, we need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations simultaneously:

[tex]\[ 5x - 7y - 21 = 0 \][/tex]
[tex]\[ 25x - 35y = 63 \][/tex]

### Step-by-Step Solution:

#### 1. Simplify the equations if possible:

First, let's simplify the second equation. We notice that both the left-hand side and right-hand side can be divided by 5:
[tex]\[ 25x - 35y = 63 \][/tex]
[tex]\[ 5(5x - 7y) = 63 \][/tex]
[tex]\[ 5x - 7y = \frac{63}{5}\][/tex]

The second equation is now:
[tex]\[ 5x - 7y = 12.6 \][/tex]

So, our system of equations becomes:
[tex]\[ 5x - 7y - 21 = 0 \][/tex]
[tex]\[ 5x - 7y = 12.6 \][/tex]

#### 2. Rewrite the first equation to match the format of the second equation for elimination:
[tex]\[ 5x - 7y = 21 \][/tex]

Now, our system is:
[tex]\[ 5x - 7y = 21 \][/tex]
[tex]\[ 5x - 7y = 12.6 \][/tex]

#### 3. Subtract the second equation from the first:
Since both left sides and the right sides are equal, we subtract the second equation from the first:
[tex]\[ (5x - 7y) - (5x - 7y) = 21 - 12.6 \][/tex]
[tex]\[ 0 = 8.4 \][/tex]

We end up with [tex]\( 0 = 8.4 \)[/tex], which is a contradiction and indicates there are no values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that can simultaneously satisfy both equations.

### Conclusion:
Hence, the given system of equations has no solution. This means the system is inconsistent.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.