3 x + 2 y + 4 z = 11
2 x - y + 3 z = 4
5 x - 3 y + 5 z = - 1
3 x + 2 y + 4 z = 11
Multiply both sides by 5
15 x + 10 y + 20 z = 55
5 x - 3 y + 5 z = - 1
Multiply both equation by 3
15 x - 9 y + 15 z = - 3
15 x + 10 y + 20 z = 55
-
15 x - 9 y + 15 z = - 3
____________________
15 x - 15 x + 10 y - ( - 9 ) y + 20 z - 15 z = 55 - ( - 3 )
10 y + 9 y + 5 z = 58
19 y + 5 z = 58
3 x + 2 y + 4 z = 11
+
2 x - y + 3 z = 4
____________________
5 x + y + 7 z = 15
5 x + y + 7 z = 15
-
5 x - 3 y + 5 z = - 1
______________________
5 x - 5 x + y - ( - 3 y ) + 7 z - 5 z = 15 - ( - 1 )
y + 3 y + 2 z = 15 + 1
4 y + 2 z = 16
Divide both sides by 2
2 y + z = 8
Subtract 2 y to both sides
2 y + z - 2 y = 8 - 2 y
z = - 2 y + 8
Replace this value in equation:
19 y + 5 z = 58
19 y + 5 ∙ ( - 2 y + 8 ) = 58
19 y + 5 ∙ ( - 2 y ) + 5 ∙ 8 = 58
19 y - 10 y + 40 = 58
9 y + 40 = 58
Subtract 40 to both sides
9 y + 40 - 40 = 58 - 40
9 y = 18
Divide both sides by 9
y = 18 / 9
y = 2
z = - 2 y + 8
z = - 2 ∙ 2 + 8
z = - 4 + 8
z = 4
Replace tis values in equation:
3 x + 2 y + 4 z = 11
3 x + 2 ∙ 2 + 4 ∙ 4 = 11
3 x + 4 + 16 = 11
3 x + 20 = 11
Subtract 20 to both sides
3 x + 20 - 20 = 11 - 20
3 x = - 9
Divide both sides by 3
x = - 9 / 3
x = - 3
The solutions are:
x = - 3 , y = 2 , z = 4
Solve the following system using elimination (aka linear combination) attach an extra sheet, if needed.
{ 3x+2y+4z=11
{ 2x-y+3z=4
{ 5x-3y+5z=-1
2 answers
My typo:
5 x - 3 y + 5 z = - 1
NOT
Multiply both equation by 3
5 x - 3 y + 5 z = - 1
Multiply both sides by 3
15 x - 9 y + 15 z = - 3
5 x - 3 y + 5 z = - 1
NOT
Multiply both equation by 3
5 x - 3 y + 5 z = - 1
Multiply both sides by 3
15 x - 9 y + 15 z = - 3