Solve the simultaneous equations 5x+4y = 1 and 3x - 6 y = 2.

x=31,y=−61

Put the equations in standard form and then use matrices to solve the system of equations.

5x+4y=1,3x−6y=2

Write the equations in matrix form.

(534−6)(xy)=(12)

Left multiply the equation by the inverse matrix of (534−6).

inverse((534−6))(534−6)(xy)=inverse((534−6))(12)

The product of a matrix and its inverse is the identity matrix.

(1001)(xy)=inverse((534−6))(12)

Multiply the matrices on the left hand side of the equal sign.

(xy)=inverse((534−6))(12)

For the 2×2 matrix (acbd), the inverse matrix is (ad−bcdad−bc−cad−bc−bad−bca), so the matrix equation can be rewritten as a matrix multiplication problem.

(xy)=(5(−6)−4×3−6−5(−6)−4×33−5(−6)−4×345(−6)−4×35)(12)

Do the arithmetic.

(xy)=(71141212−425)(12)

Multiply the matrices.

(xy)=(71+212×2141−425×2)

Do the arithmetic.

(xy)=(31−61)

Extract the matrix elements x and y.

x=31,y=−61

First equation: x= 1 y= -1

Second equation:  x = 2/3 y = 1/-3

Step-by-step explanation:

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%

it's d

step-by-step explanation: