Question

Solve ax + by -2 and a2x + b2y = a + b. given a and b are non-zero constants such that a is not equal to b

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{ax+by=2}$

$\mathsf{a^2x+b^2y=a+b}$

$\underline{\textsf{To find:}}$

$\textsf{The solution of the given equations}$

$\underline{\textsf{Solution:}}$

$\textsf{We apply the cross mutiplication rule to}$

$\textsf{given linear equations}$

$\mathsf{ax+by-2=0}$

$\mathsf{a^2x+b^2y-(a+b)=0}$

$\textsf{By cross multiplication rule}$

$\mathsf{\dfrac{x}{-b(a+b)+2b^2}=\dfrac{y}{-2a^2+a(a+b)}=\dfrac{1}{ab^2-a^2b}}$

$\mathsf{\dfrac{x}{-ab+b^2+2b^2}=\dfrac{y}{-2a^2+a^2+ab)}=\dfrac{1}{ab(b-a)}}$

$\mathsf{\dfrac{x}{b(b-a)}=\dfrac{y}{a(b-a)}=\dfrac{1}{ab(b-a)}}$

$\mathsf{\dfrac{x}{b}=\dfrac{y}{a}=\dfrac{1}{ab}}$

$\implies\mathsf{\dfrac{x}{b}=\dfrac{1}{ab}}$

$\mathsf{x=\dfrac{b}{ab}=\dfrac{1}{a}}$

$\textsf{and}$

$\mathsf{\dfrac{y}{a}=\dfrac{1}{ab}}$

$\mathsf{y=\dfrac{a}{ab}=\dfrac{1}{b}}$

$\underline{\textsf{Answer:}}$

$\textsf{The solution is}$

$\mathsf{x=\dfrac{1}{a},\;y=\dfrac{1}{b}}$

Find more:

Solve each of the following systems of equations by the method of cross-multiplication:

ax + by = a²

bx + ay = b²

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Solve each of the following systems of equations by the method of cross-multiplication:

a²x+b²y=c²b²x+a²y=a²

https://brainly.in/question/15918831