how do you solve (3x+2y=17 -2x+4y=7) in matrix form?

Question

this one is from matrices calculus. i need it solved. you can follow engineering maths book edition 1,2,3,4,5.

Answer 1

Create the determinant from the variable coefficients:

|  3 2 |

| -2 4 |=3×4-(2×-2)=12+4=16, let Δ=16.

Create two more determinants for x and y, substituting the constants in place of the relevant coefficients:

Δ_x=

| 17 2 |

|   7 4 |=17×4-2×7=68-14=54,

x=Δ_x/Δ=54/16=27/8.

Δ_y=

|  3 17 |

| -2   7 |=3×7-(17×-2)=21+34=55,

y=Δ_y/Δ=55/16.

SOLUTION is x=27/8, y=55/16.