Solve the equations for x and y 2x-y=1 ;4x-7y=-2
Answers
Answer:
.
Step-by-step explanation:
Given:
A linear equation in two variable.
To solve for x & y .
{\underline{\underline{\red{\sf{To\:Find}}}}}ToFind
Value of x and y .
We have to solve by cross multiplication method.
{\underline{\underline{\red{\sf{Concept\:Used}}}}}ConceptUsed
We will use the formula of 'Method of Cross-multiplication ' for finding the values of x and y .
{\underline{\underline{\red{\sf{Answer:}}}}}Answer:
We have been given two linear equations which are
\sf{4x-3y-1=0}4x−3y−1=0
\sf{5x-7y+2=0}5x−7y+2=0
\sf{\pink{With\:respect\:to\:Standard\:Form}}WithrespecttoStandardForm
\sf{ a_{1}=4\:\:\:\:\:\:\:b_{1}=(-3)\:\:\:\:\:\:\:c_{1}=(-1)}a1=4b1=(−3)c1=(−1)
\sf{ a_{2}=5\:\:\:\:\:\:\:b_{2}=(-7)\:\:\:\:\:\:\:c_{2}=(2)}a2=5b2=(−7)c2=(2)
{\underline{\purple{\sf{The\:formula\:is\: stated\:as}}}}Theformulaisstatedas
\large\red{\boxed{\blue{\bf{\dfrac{x}{(b_{1}c_{2}-b_{2}c_{1})}=\dfrac{y}{c_{1}a_{2}-c_{2}a_{1}}=\dfrac{1}{a_{1}b_{2}-a_{2}b_{1}}}}}}(b1c2−b2c1)x=c1a2−c2a1y=a1b2−a2b11
\sf{\green{On\: putting\: the\:values}}Onputtingthevalues
\sf{\implies \dfrac{x}{(-3\times2)-(-1\times-7)}=\dfrac{y}{(4\times2)-(5\times(-1))}=\dfrac{1}{(7\times(-4))-(-5\times3)}}⟹(−3×2)−(−1×−7)x=(4×2)−(5×(−1))y=(7×(−4))−(−5×3)1
\sf{\implies \dfrac{x}{-6-7}=\dfrac{y}{8+5}=\dfrac{1}{-28+15}}⟹−6−7x=8+5y=−28+151
\sf{\implies \dfrac{x}{-13}=\dfrac{y}{13}=\dfrac{1}{-13}}⟹−13x=13y=−131
\sf{\implies \dfrac{x}{-13}=\dfrac{1}{-13}}⟹−13x=−131
{\underline{\boxed{\orange{\sf{\mapsto x =1}}}}}↦x=1