What are the values of x y and z in 2x plus 5y-3z equals 4 and 3x-2y equals 0 and 7x-4y-5z equals -23 showing all work by elimination and finally by substitution?

Answer 1

Equations: 2x+5y-3z = 4 and 3x-2y = 0 and 7x-4y-5z = -23 their solutions are:-

5*(2x+5y-3z =4) => 10x+25y-15z = 20

3*(7x-4y-5z = -23) => 21x-12y-15z = -69

Subtracting the above: -11x+37y = 89 thus eliminating z

3*(-11x+37y = 89) => -33x+111y = 267

11*(3x-2y = 0) => 33x-22y = 0

Adding the above: 89y = 267 thus eliminating x

If: 89y = 267 then y = 267/89 => 3

So by substitution: x = 2, y = 3 and z = 5

Check: (2*2)+(5*3)-(3*5) = 4

Check: (3*2)-(2*3) = 0

Check: (7*2)-(4*3)-(5*5) = -23