How do you solve the following system: 3x - 4y = -10, 4x + 7y = 6x?

Feb 8, 2016

$x = - \frac{70}{13} \text{ }$I have left the derivation of y for the reader to determine.

Explanation:

Given:

$3 x - 4 y = - 10 \text{ }$.................................(1)
$4 x + 7 y = 6 x \text{ }$......................................(2)
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Consider equation (2)

Subtract $4 x$ from both sides

$7 y = 2 x$

Divide both sides by 7

$y = \frac{2}{7} x \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left({2}_{a}\right)$

Substitute $\left({2}_{a}\right) \text{ into } \left(1\right)$

$3 x - 4 \left(\frac{2}{7} x\right) = - 10 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$

$3 x - \frac{8}{7} x = - 10$

$x \frac{21 - 8}{7} = - 10$

$x = - \left(\frac{7}{13} \times 10\right)$

$x = - \frac{70}{13} \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \left({1}_{b}\right)$
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You can now find $y$ by substituting $\left({1}_{b}\right)$ into either of (1) or (2).

I will leave that for the reader to do