Find the truth set of the following simultaneous equation {:(5x)/(6)-3//4quad y=1//2×2//3quad y=(5)/(2):}

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

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Find the truth set of the following simultaneous equation

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

Find the truth set of the following simultaneous equation $\newline$ $\frac{5x}{6}-\frac{3}{4}$ $y=\frac{1}{2}\times\frac{2}{3}$ $y=\frac{5}{2}$

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Q. Find the truth set of the following simultaneous 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: $\newline$ $x = \frac{159}{40}$