Solve {l}{H_{1}=70.29-60*0.002+60*0.003=}{H_{2}=70.29-20*0.002+60*0.003=}{H_{3}=70.29+20*0.002+60*0.003=}{H_{4}=70.29+60*0.002+60*0.003=}

$$\left. \begin{array} { l } { H _ { 1 } = 70.29 - 60 \times 0.002 + 60 \times 0.003 = } \\ { H _ { 2 } = 70.29 - 20 \times 0.002 + 60 \times 0.003 = } \\ { H _ { 3 } = 70.29 + 20 \times 0.002 + 60 \times 0.003 = } \\ { H _ { 4 } = 70.29 + 60 \times 0.002 + 60 \times 0.003 = } \end{array} \right.$$

Solve for H_1, H_2, H_3, H_4

$$H_{1}=70.35$$

$$H_{2}=70.43$$

$$H_{3}=70.51$$

$$H_{4}=70.59$$

Solution Steps

Consider the first equation. Multiply 60 and 0.002 to get 0.12.

$$H_{1}=70.29-0.12+60\times 0.003$$

Subtract 0.12 from 70.29 to get 70.17.

$$H_{1}=70.17+60\times 0.003$$

Multiply 60 and 0.003 to get 0.18.

$$H_{1}=70.17+0.18$$

Add 70.17 and 0.18 to get 70.35.

$$H_{1}=70.35$$

Consider the second equation. Multiply 20 and 0.002 to get 0.04.

$$H_{2}=70.29-0.04+60\times 0.003$$

Subtract 0.04 from 70.29 to get 70.25.

$$H_{2}=70.25+60\times 0.003$$

Multiply 60 and 0.003 to get 0.18.

$$H_{2}=70.25+0.18$$

Add 70.25 and 0.18 to get 70.43.

$$H_{2}=70.43$$

Consider the third equation. Multiply 20 and 0.002 to get 0.04.

$$H_{3}=70.29+0.04+60\times 0.003$$

Add 70.29 and 0.04 to get 70.33.

$$H_{3}=70.33+60\times 0.003$$

Multiply 60 and 0.003 to get 0.18.

$$H_{3}=70.33+0.18$$

Add 70.33 and 0.18 to get 70.51.

$$H_{3}=70.51$$

Consider the fourth equation. Multiply 60 and 0.002 to get 0.12.

$$H_{4}=70.29+0.12+60\times 0.003$$

Add 70.29 and 0.12 to get 70.41.

$$H_{4}=70.41+60\times 0.003$$

Multiply 60 and 0.003 to get 0.18.

$$H_{4}=70.41+0.18$$

Add 70.41 and 0.18 to get 70.59.

$$H_{4}=70.59$$

The system is now solved.

$$H_{1}=70.35 H_{2}=70.43 H_{3}=70.51 H_{4}=70.59$$