How do solve the following linear system?: $- 10 x + 7 y = - 2, - 4 x - 15 y = - 1$ $-10x+7y=-2 , -4x-15y=-1$ ?

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Answer 1 · 2016-03-05T05:48:07

$x = \frac{37}{178}$ $x = 37/178$
$y = \frac{1}{89}$ $y = 1/89$

Scale either equation (or both) with the goal of eliminating one of the variables

$[1] - 10 x + 7 y = - 2$ $[1] -10x + 7y = -2$

$[2] - 4 x - 15 y = - 1$ $[2] -4x - 15y = -1$

Multiply $[1]$ $[1]$ by -2 and multiply $[2]$ $[2]$ by 5

$[1'] -2(-10x + 7y = -2)$

$=> [1'] 20x -14y = 4$

$[2'] 5(-4x - 15y = -1)$

$=> [2'] -20x - 75y = -5$

$[1'] 20x -14y = 4$
$[2'] -20x - 75y = -5$

If we add both equations, $x$ will be eliminated and we can solve for y

$[3] -89y = -1$

$=> y = 1/89$

To get $x$ , substitute the obtained value for $y$ in one of the equations $[1]$ , $[1']$ , $[2]$ , $[2']$ . For example, let's use $[1]$

$-10x + 7y = -2$

$=> -10x + 7(1/89) = -2$

$=:> -10x + 7/89 = -2$

$=> 10x = 2 + 7/89$

$=> 10x = (178 + 7)/89$

$=> 10x = 185/89$

$=> x = 37/178$

How do solve the following linear system?: -10x+7y=-2 , -4x-15y=-1 −10x+7y=−2,−4x−15y=−1 -10x+7y=-2 , -4x-15y=-1 ?