Let 2x−y+3z=7 1st equation
Let 5x−4y−2z=3 2nd equation
Let 4x+y−2z=−4 3rd equation
Use 3rd equation so that y in terms of x and z
y=−4+2z−4x 3rd equation
Use now 1st and 3rd
2x−y+3z=7 1st equation
2x−(−4+2z−4x)+3z=7
2x+4−2z+4x+3z=7
2x+4x−2z+3z=7−4
6x+z=3 Let this be the 4th equation
Use 2nd and 3rd equations:
5x−4y−2z=3 2nd equation
5x−4(−4+2z−4x)−2z=3
5x+16−8z+16x−2z=3
5x+16x−8z−2z=3−16
21x−10z=−13 Let this be the 5th equation
Solve for x and z using 4th and 5th equations
From 4th equation: z=3−6x insert in 5th equation
21x−10z=−13 5th equation
21x−10(3−6x)=−13
21x−30+60x=−13
81x=30−13
81x=17
x=1781
Go back to the 4th equation , use x=1781
From 4th equation: z=3−6x
z=3−6⋅1781
z=4727
Go back to the 3rd equation and use x=1781 and z=4727
y=−4+2z−4x 3rd equation
y=−4+2⋅4727−4⋅1781
y=−11081
The solution set:
x=1781
y=−11081
z=4727
have a nice day from the Philippines!
