Solve each system of equations using thesubstitution method. 1) { x 2 + z 2 = 5

Question

Solve each system of equations using thesubstitution method. 1) { x2 + z2 = 5     { 2x + y = 1    { y + z = 1 *the answer is (1, -1, 2), (-1, 3, -2) 2) The perimeter of a rectangle is 40 inches, and its area is96 in2. Find its lenth and width. *the answer is 12 in. x 8 in. Solve each system of equations using thesubstitution method. 1) { x2 + z2 = 5     { 2x + y = 1    { y + z = 1 *the answer is (1, -1, 2), (-1, 3, -2) 2) The perimeter of a rectangle is 40 inches, and its area is96 in2. Find its lenth and width. *the answer is 12 in. x 8 in.

Explanation / Answer

1) { x2 + z2 = 5     { 2x + y = 1  2x=1-y      x=(1-y)/2
   { y + z = 1    z=1-y        z=2x

so first equation=
x^2+(2x)^2=5
5x^2=5
x^2=1
x=+-1

if x=-1, z=-2 and y= 3
if x=1   z=2   and y=-1

2) The perimeter of a rectangle is 40 inches, and its area is96 in2. Find its lenth and width. 2w+2l=40
w+l=20 l=20-w

wl=96
w(20-w)=96
w^2-20w+96=0
w=12 or 8

w+l=20 so if you put either 12 or 8 youll get 8or12 which is thesame combination

*the answer is 12 in. x 8 in.

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