Question

.IfA=(5 3

7 5),X=(x

y)andC=(-5

11)andifAX=C.Thenfindthevaluesof

xandy​

Answer 1

Answer: x = -14.5 ; y = 22.5

Given question is a matrix based question.

$A = \left[\begin{array}{cc}5&3\\7&5\end{array}\right] \\\\\\X = \left[\begin{array}{cc}x\\y\end{array}\right]\\\\\\C = \left[\begin{array}{cc}-5\\11\end{array}\right]$

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:

$\implies AX = C\\\\\\\implies \left[\begin{array}{cc}5x+3y\\7x+5y\end{array}\right] = \left[\begin{array}{cc}-5\\11\end{array}\right]$

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.