+26396 x + y + z = 11
0.70x + 0.55y + 0.50z = 6.70
x = 3z
(1)x+y+z=11(2)0.70x+0.55y+0.50z=6.70x=3z:(1)3z+y+z=11(2)0.70⋅(3z)+0.55y+0.50z=6.70(1)y+4z=11(2)2.1⋅z+0.55y+0.50z=6.70(1)y+4z=11(2)0.55y+2.60z=6.70(1)y=11−4z(2)0.55y+2.60z=6.700.55(11−4z)+2.60z=6.700.55⋅11−0.55⋅4z+2.60z=6.706.05−2.20z+2.60z=6.706.05+0.40z=6.700.40z=6.70−6.050.40z=0.65z=0.650.40z=1.625(1)y=11−4zy=11−4⋅1.625y=11−6.5y=4.5x=3zx=3⋅1.625x=4.875
+26396 x + y + z = 11
0.70x + 0.55y + 0.50z = 6.70
x = 3z
(1)x+y+z=11(2)0.70x+0.55y+0.50z=6.70x=3z:(1)3z+y+z=11(2)0.70⋅(3z)+0.55y+0.50z=6.70(1)y+4z=11(2)2.1⋅z+0.55y+0.50z=6.70(1)y+4z=11(2)0.55y+2.60z=6.70(1)y=11−4z(2)0.55y+2.60z=6.700.55(11−4z)+2.60z=6.700.55⋅11−0.55⋅4z+2.60z=6.706.05−2.20z+2.60z=6.706.05+0.40z=6.700.40z=6.70−6.050.40z=0.65z=0.650.40z=1.625(1)y=11−4zy=11−4⋅1.625y=11−6.5y=4.5x=3zx=3⋅1.625x=4.875
x + y + z = 11
0.70x + 0.55y + 0.50z = 6.70
x = 3z
Solve the following system:
{y+4 z = 11 | (equation 1)
0.55 y+2.6 z = 6.7 | (equation 2)
Subtract 0.65 × (equation 1) from equation 2:
{4 z+y = 11 | (equation 1)
0 z-0.1 y = -0.45 | (equation 2)
Divide equation 2 by -1.:
{4 z+y = 11 | (equation 1)
0 z+0.1 y = 0.45 | (equation 2)
Divide equation 2 by 0.1:
{4 z+y = 11 | (equation 1)
0. z+y = 4.5 | (equation 2)
Subtract equation 2 from equation 1:
{4 z+0 y = 6.5 | (equation 1)
0 z+y = 4.5 | (equation 2)
Divide equation 1 by 4:
{z+0 y = 1.625 | (equation 1)
0 z+y = 4.5 | (equation 2)
Collect results:
Answer: |
| {z = 1.625
y = 4.5
x=1.625 X 3=4.875
