3a-5b:3a+5b=1:4 find the value of a and b

a = 5/6 , b = -3/10

Step-by-step explanation:

3a-5b:3a+5b=1:4

3a-5b / 3a +5b = 1/4

Cross multiply

3a -5b =4 (1)            solve simultaneously

3a + 5b = 1 (2)    using elimination method

Add equation 1 and 2

6a = 5

Divide both sides by 6

6a/6 = 5/6

a =5/6

Put value of a into equation 2

3a +5b = 1

3(5/6) + 5b = 1

5/2 + 5b = 1

5b = 1 -  5/2

5b = - 1½

5b = - 3/2

Divide both sides by 5

5b/ 5 = -3/2 ÷ 5

b = -3/2 × ¹/5

b = - 3/10

Therefore a = 5/6 , b = -3/10

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