solve matrix 4x-7y=2 and 3x+5y=9

Question

please write a matrix equation for the system of equation

and if you want help me with this one 2a+3b-5c=1, 7a+3c=7  and 3a-6b+c=-5

~thank you so much.

Answer 1

Given equations are 4x-7y = 2 ---> (1)

3x+5y = 9 ---> (2)

Convert the above equations in to matrix form.

We solve the equations in cramer's method.

AX = B

A is coefficient matrix, B is constant matrix and X is variable matrix.

DetA = 20+21 = 41

= 10+63 = 73

= 36-6 = 30

Solution x = 73/41 and y = 30/41.

Answer 2

Given equations are 2a+3b-5c = 1 ---> (1)

7a+3c = 7 ---> (2)

3a-6b+c = -5 ---> (3)

Convert the above equations in to matrix form.

We solve the equations in cramer's method.

AX = B

A is coefficient matrix, B is constant matrix and X is variable matrix.

= 2(0+18)-3(7-9)-5(-42-0)

= 36+6+210 = 252

1(0+18)-3(7+15)-5(-42+0)

= 18-66+210 = 162

2(7+15)-1(7-9)-5(-35-21)

= 44+2+280 = 326

2(0+42)-3(-35-21)+1(-42-0)

= 84+168-42 = 210

a = 162/252, b = 326/252, c = 210/252

Solution a = 81/126, b = 163/126, c = 105/126.