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Find the treth set of the following simultaneus equation

{:(5x)/(6)-3//4quad y=1//2×2//3quad y=(5)/(2):}

Page No. $\newline$ Date: $\newline$ Find the treth set of the following simultaneus equation $\newline$ ${\frac{5x}{6}-\frac{3}{4}y=\frac{1}{2}\times\frac{2}{3}y=\frac{5}{2}}$

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Find indefinite integrals using the substitution

Full solution

Q. Page No.

\newline

Date:

\newline

Find the treth set of the following simultaneus equation

\newline

{\frac{5x}{6}-\frac{3}{4}y=\frac{1}{2}\times\frac{2}{3}y=\frac{5}{2}}

Simplify Equations: Simplify the equations: $\newline$ First equation: $(\frac{5x}{6} - \frac{3}{4} y = \frac{1}{2})$ $\newline$ Second equation: $(\frac{2}{3} y = \frac{5}{2})$
Solve for y: Solve the second equation for y: $\newline$ $\frac{2}{3} y = \frac{5}{2}$ $\newline$ Multiply both sides by $\frac{3}{2}$ to isolate y: $\newline$ $y = \left(\frac{5}{2}\right) \times \left(\frac{3}{2}\right) = \frac{15}{4}$
Substitute y into First Equation: Substitute $y = \frac{15}{4}$ into the first equation: $\newline$ $\frac{5x}{6} - \frac{3}{4} \times \frac{15}{4} = \frac{1}{2}$ $\newline$ $\frac{5x}{6} - \frac{45}{16} = \frac{1}{2}$
Solve for x: Solve for x: $\newline$ First, convert $\frac{1}{2}$ to a fraction with a denominator of $16$ : $\newline$ $\frac{1}{2} = \frac{8}{16}$ $\newline$ Now, add $\frac{45}{16}$ to both sides: $\newline$ $\frac{5x}{6} = \frac{8}{16} + \frac{45}{16}$ $\newline$ $\frac{5x}{6} = \frac{53}{16}$ $\newline$ Multiply both sides by $\frac{6}{5}$ to solve for x: $\newline$ $x = \frac{53}{16} \cdot \frac{6}{5} = \frac{318}{80}$ $\newline$ Simplify x: $\newline$ $x = \frac{159}{40}$

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