Math, asked by gunjant183, 9 months ago




can any please help me in this questions​

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Answers

Answered by rimisaha318
0

Answer:

,

Step-by-step explanation:

 \frac{4(7 + x) - 5(2x - y)}{20}  = 3y - 5

 \frac{28 + 4x - 10x + 5y}{20}  = 3y - 5

28 - 6x + 5y = 60y - 100

128 = 6x - 55y

6x - 55y = 128

x - y =  \frac{128}{55 \times 6}

x - y =  \frac{64}{165}

Answered by varadad25
2

Question:

Solve:

\displaystyle{\sf\:\dfrac{x\:+\:7}{5}\:-\:\dfrac{2x\:-\:y}{4}\:=\:3y\:-\:5}

\displaystyle{\sf\:\dfrac{5y\:-\:7}{2}\:+\:\dfrac{4x\:-\:3}{6}\:=\:18\:-\:5x}

Answer:

\displaystyle{\boxed{\red{\sf\:(\:x\:,\:y\:)\:=\:(\:3\:,\:2\:)\:}}}

Step-by-step-explanation:

The given linear equations are

\displaystyle{\sf\:\dfrac{x\:+\:7}{5}\:-\:\dfrac{2x\:-\:y}{4}\:=\:3y\:-\:5}

\displaystyle{\implies\sf\:\dfrac{4\:(\:x\:+\:7\:)\:-\:5\:(\:2x\:-\:y\:)}{5\:\times\:4}\:=\:3y\:-\:5}

\displaystyle{\implies\sf\:\dfrac{4x\:+\:28\:-\:10x\:+\:5y}{20}\:=\:3y\:-\:5}

\displaystyle{\implies\sf\:4x\:-\:10x\:+\:28\:+\:5y\:=\:20\:(\:3y\:-\:5\:)}

\displaystyle{\implies\sf\:-\:6x\:+\:28\:+\:5y\:=\:60y\:-\:100}

\displaystyle{\implies\sf\:28\:+\:100\:=\:6x\:+\:60y\:-\:5y}

\displaystyle{\implies\sf\:6x\:+\:55y\:=\:128}

\displaystyle{\implies\sf\:6x\:=\:128\:-\:55y}

\displaystyle{\implies\:\boxed{\blue{\sf\:x\:=\:\dfrac{128\:-\:55y}{6}}}\sf\:\quad\cdots\:(\:1\:)}

And,

\displaystyle{\sf\:\dfrac{5y\:-\:7}{2}\:+\:\dfrac{4x\:-\:3}{6}\:=\:18\:-\:5x}

\displaystyle{\implies\sf\:\dfrac{5y\:-\:7}{2}\:\times\:\dfrac{3}{3}\:+\:\dfrac{4x\:-\:3}{6}\:=\:18\:-\:5x}

\displaystyle{\implies\sf\:\dfrac{15y\:-\:21}{6}\:+\:\dfrac{4x\:-\:3}{6}\:=\:18\:-\:5x}

\displaystyle{\implies\sf\:\dfrac{15y\:-\:21\:+\:4x\:-\:3}{6}\:=\:18\:-\:5x}

\displaystyle{\implies\sf\:15y\:+\:4x\:-\:24\:=\:6\:(\:18\:-\:5x\:)}

\displaystyle{\implies\sf\:15y\:+\:4x\:-\:24\:=\:108\:-\:30x}

\displaystyle{\implies\sf\:15y\:+\:4x\:+\:30x\:=\:108\:+\:24}

\displaystyle{\implies\sf\:15y\:+\:34x\:=\:132}

\displaystyle{\implies\sf\:15y\:+\:34\:\times\:\dfrac{128\:-\:55y}{6}\:=\:132\:\sf\:\quad\cdots\:[\:From\:(\:1\:)\:]}

\displaystyle{\implies\sf\:15y\:+\:\dfrac{4352\:-\:1870y}{6}\:=\:132}

\displaystyle{\implies\sf\:\dfrac{90y\:+\:4352\:-\:1870y}{6}\:=\:132}

\displaystyle{\implies\sf\:90y\:-\:1870y\:+\:4352\:=\:132\:\times\:6}

\displaystyle{\implies\sf\:-\:1780y\:+\:4352\:=\:792}

\displaystyle{\implies\sf\:1780y\:=\:4352\:-\:792}

\displaystyle{\implies\sf\:1780y\:=\:3560}

\displaystyle{\implies\sf\:y\:=\:\dfrac{356\:\cancel{0}}{178\:\cancel{0}}}

\displaystyle{\implies\sf\:y\:=\:\dfrac{\cancel{356}}{\cancel{178}}}

\displaystyle{\implies\sf\:y\:=\:\dfrac{\cancel{178}}{\cancel{89}}}

\displaystyle{\implies\:\boxed{\green{\sf\:y\:=\:2}}}

Now,

\displaystyle{\sf\:x\:=\:\dfrac{128\:-\:55y}{6}}

\displaystyle{\implies\sf\:x\:=\:\dfrac{128\:-\:55\:\times\:2}{6}}

\displaystyle{\implies\sf\:x\:=\:\dfrac{128\:-\:110}{6}}

\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{18}{6}}}

\displaystyle{\implies\:\boxed{\pink{\sf\:x\:=\:3}}}

\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:(\:x\:,\:y\:)\:=\:(\:3\:,\:2\:)}}}}

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