Question

Solve the following system of linear equations

​2(ax - by) + (a + 4b) = 0

2(bx + ay) + (b - 4a) =0​

Answer 1

Step-by-step explanation:

multiply equation 1 by b

multiply equation 2 by a,

• 2abx - 2b²y + a²+4ab=0......(1)
• 2abx +2a²y+ ab- 4a² =0......(2)

subtract 1 and 2

• (2abx-2abx)-2b²y-2a²y+a²+4ab-ab²+4a²=0
• -2y(a²+b²)+5a²+3ab²=0
• -2y(a²+b²)=a(5a+3b)
• y=a(5a+3b)/2(a²+b²)

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Answer 2

Step-by-step explanation:

multiply equation 1 by b

multiply equation 2 by a,

2abx - 2b²y + a²+4ab=0......(1)

2abx +2a²y+ ab- 4a² =0......(2)

subtract 1 and 2

(2abx-2abx)-2b²y-2a²y+a²+4ab-ab²+4a²=0

-2y(a²+b²)+5a²+3ab²=0

-2y(a²+b²)=a(5a+3b)

y=a(5a+3b)/2(a²+b²)