Let's solve the given equation step-by-step:
[tex]\[ 10x - 5y = 15y - 25x \][/tex]
1. Start by bringing all terms involving [tex]\(x\)[/tex] to one side and all terms involving [tex]\(y\)[/tex] to the other side. Add [tex]\(25x\)[/tex] to both sides:
[tex]\[ 10x + 25x - 5y = 15y \][/tex]
2. Combine the [tex]\(x\)[/tex] terms on the left side:
[tex]\[ 35x - 5y = 15y \][/tex]
3. Next, add [tex]\(5y\)[/tex] to both sides to bring all the [tex]\(y\)[/tex] terms to the right side:
[tex]\[ 35x = 20y \][/tex]
4. Now, to isolate [tex]\(x\)[/tex], we divide both sides of the equation by 35:
[tex]\[ x = \frac{20y}{35} \][/tex]
5. Simplify the fraction [tex]\(\frac{20y}{35}\)[/tex]:
[tex]\[ x = \frac{4y}{7} \][/tex]
So, the solution to the equation is:
[tex]\[ x = \frac{4y}{7} \][/tex]
This means that for any value of [tex]\(y\)[/tex], [tex]\(x\)[/tex] will be [tex]\(\frac{4}{7}\)[/tex] times that value of [tex]\(y\)[/tex].
