Question

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Explanation:

For System 7:

Step1: Rearrange first equation

$14m - 3n = 8$

Step2: Simplify second equation

Divide by 2: $14m - 3n = 6$

Step3: Analyze consistency

The left sides are identical, but $8
eq 6$, so no solution exists.

For System 8:

Step1: Rearrange first equation

$20u - 5v = 11$

Step2: Isolate $v$ from second equation

$v = 22 - 6u$

Step3: Substitute $v$ into first equation

$20u - 5(22 - 6u) = 11$
$20u - 110 + 30u = 11$
$50u = 121$

Step4: Solve for $u$

$u = \frac{121}{50} = 2.42$

Step5: Solve for $v$

$v = 22 - 6\times\frac{121}{50} = 22 - \frac{726}{50} = \frac{1100 - 726}{50} = \frac{374}{50} = \frac{187}{25} = 7.48$

Answer:

1. No solution (the system is inconsistent)
2. $u=\frac{121}{50}$, $v=\frac{187}{25}$ (or $u=2.42$, $v=7.48$)