Question

5x - y + z = -6
2x + 7y + 3z = 8
x + 2z = 6

Answer 1

Explanation:

The system of equations given are:

5x - y + z = -6 ------------- i

2x + 7y + 3z = 8 ---------- ii

x + 2z = 6 ----------------- iii

Let us deal with equation i and ii first since they have 3 variables x, y and z;

5x - y + z = -6 x 7

2x + 7y + 3z = 8 x 1

35x - 7y + 7z = -42 ---- iv

2x + 7y + 3z = 8 ---- v

Add equation iv and v;

37x + 10z = -34 ------vi

So, let us solve equation vi and iii:

x + 2z = 6 - ---------- iii x 10

37x + 10z = -34 --- iv x 2

10x + 20z = 60 vi

74x + 20z = -68 vii

Subtract vi - vii;

-64x = 128

x = -2

So; put x = -2 into iii;

x + 2z = 6

-2 + 2z = 6

2z = 6 + 2 = 8

z = 4

Put x = -2 and z = 4 into equation i;

5(-2) - y + 4 = - 6

-10 -y +4 = -6

-6 - y = -6

-y = 0

y = 0