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2 votes
Solve the system by back substitution.

- 2x - 4y - z- 3w = -5
-2y - 12z - 4w = - 16
5z +5w=10
4w =12

User RobinJoe
by
5.5k points

1 Answer

4 votes

Answer:

y=8 x=-19.5

Explanation:


Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8


Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:


2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5

User Jason Hall
by
5.6k points
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