.IfA=(5 3
7 5),X=(x
y)andC=(-5
11)andifAX=C.Thenfindthevaluesof
xandy
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Answer: x = -14.5 ; y = 22.5
Given question is a matrix based question.
According to the question, AX = C. Using this, we are required to find the values of x & y.
Matrix multiplication of AX = C would give:
Therefore we get a pair of linear equation in 2 variables.
- 5x + 3y = -5
- 7x + 5y = 11
Solving this we get:
→ 7x = 11 - 5y
→ x = ( 11 - 5y ) / 7 ...(i)
Substituting (i) in first equation we get:
→ 5 ( 11 - 5y ) / 7 + 3y = -5
→ ( 55 - 25y ) / 7 + 3y = -5
Taking LCM we get:
→ ( 55 - 25y + 21y ) / 7 = -5
→ ( 55 - 4y ) = -35
→ 55 + 35 = 4y
→ 90 = 4y
→ y = 90/4
→ y = 22.5
Substituting value of 'y' in (i) we get:
→ x = ( 11 - 5 ( 22.5 ) ) / 7
→ x = ( 11 - 112.5 ) / 7
→ x = ( -101.5 ) / 7
→ x = -14.5
Hence the values of 'x' and 'y' are 22.5 and -14.5 respectively.
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