Solve that each of the following system of equation has a unique solution and solve it question no one 3x +5y=12;5x+3y=4
Answers
Answer:
x = -1 and y = 3
Step-by-step explanation:
The given system of equations is:
3x + 5y = 12 5x + 3y = 4
These equations are of the forms:
a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0
where, a1 = 3, b1= 5, c1 = -12 and a2 = 5, b2 = 3, c2 = -4
For a unique solution, we must have:
a1/a2 ≠ b1/b2, i.e.,3/5 ≠ 5/3
Hence, the given system of equations has a unique solution.
Again, the given equations are:
3x + 5y = 12 …..(i)
5x + 3y = 4 …..(ii)
On multiplying (i) by 3 and (ii) by 5, we get:
9x + 15y = 36 …….(iii)
25x + 15y = 20 ……(iv)
On subtracting (iii) from (iv), we get:
16x = -16
⇒x = -1
On substituting x = -1 in (i), we get:
3(-1) + 5y = 12
⇒5y = (12 + 3) = 15
⇒y = 3
Hence, x = -1 and y = 3 is the required solution.
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Answer:
x = -1 and y = 3
this correct answer