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$Y=\frac{4}{7}x$ $\newline$ $\frac{2}{3}x=y+\frac{5}{7}$

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Solve equations with variables on both sides: fractional coefficients

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Q.

Y=\frac{4}{7}x

\newline

\frac{2}{3}x=y+\frac{5}{7}

Express $y$ in terms of $x$ : First, we need to express $y$ from the first equation in terms of $x$ . $\newline$ $Y = \frac{4}{7}x$ $\newline$ This equation shows that $y$ is a fraction of $x$ , specifically $\frac{4}{7}$ of it.
Substitute into second equation: Next, we substitute the expression for $y$ from the first equation into the second equation. $\newline$ $\frac{2}{3}x = \left(\frac{4}{7}x\right) + \frac{5}{7}$ $\newline$ This allows us to have an equation with only one variable, $x$ .
Combine x terms: Now, we need to solve for $x$ . To do this, we first need to get all terms involving $x$ on one side of the equation. $\frac{2}{3}x - \frac{4}{7}x = \frac{5}{7}$ We subtract $\frac{4}{7}x$ from both sides to combine $x$ terms.
Find common denominator: To combine the fractions, we need a common denominator. The common denominator for $3$ and $7$ is $21$ . $\newline$ $(\frac{14}{21})x - (\frac{12}{21})x = \frac{5}{7}$ $\newline$ We multiply the numerators by the necessary values to get the common denominator.
Combine $x$ terms: Now we combine the $x$ terms. $\frac{14}{21}x - \frac{12}{21}x = \frac{2}{21}x$ So, $\frac{2}{21}x = \frac{5}{7}$
Isolate x: Next, we solve for x by isolating it on one side. $\newline$ $(\frac{2}{21})x = \frac{5}{7}$ $\newline$ To isolate x, we multiply both sides by the reciprocal of $(\frac{2}{21})$ , which is $(\frac{21}{2})$ . $\newline$ $x = (\frac{5}{7}) \times (\frac{21}{2})$
Perform multiplication: Now we perform the multiplication to solve for $x$ . $x = (5 \times 21) / (7 \times 2)$ $x = 105 / 14$ $x = 7.5$

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