Given
1 ) x + 2y -2z =3
we will solve the above by letting Z be the subjet o our eqution as follows :
-2z = 3 -x -2y
Z = (-x /-2 ) -( 2y/-2) + (3 /-2) .{ divide by -2 both sides)
z = 1/2x -y -3/2
2)3x +y +z =8
z = -3x -y +8 ......{ set z as a subject of the formula )
since we have 2 equation we can equate , and cancel the variable that is
x + 2y -2z =3
3x + y + z =8
= 5x + 3y -z = 11 {I have added the two equation to get equation 3 )
lets multiply equation 3 by 2 , and add it to equation 1
2 *(5x + 3y -z )= 11
10 x +6y -2Z = 22 .....add to equation 1
x + 2y -2z = 3
11x +8y = 3
• we will now take the first equation and sutract x
x + 2y -2z =3
2y -2z +x = 3 -x ( then subtract x )
→ 2y -2z= 3-x (divide by 2 )
y -z = (3-x /2)
y = (3-x/2) + z ..... take this equation and substitute into equation 2
• 3x + y + z =8
3x + (3-x/2) + z +z = 8 .... we know that