Given: a mod 7 = 5 and b mod 7 = 6 Find (a + b)mod 7. Do not use specific numbers for a and b. Consider a, b as generic particulars. Show steps but you do not need to provide reasons.(7 points)

wouldn't it be 77

Step-by-step explanation:

If 7 = 5 is a and 7 = 6 is b and you add them you will get 11 then multiply it by 7 which would give you 77

or If you add 7 + 7 = 14 multiply 11

Or the answer is 154

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