How do solve the following linear system?: $2x-y=4 , 3x – 4y = 7$ ?

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Answer 1 · 2017-02-03T05:25:53

$x=9/5$
$y=-2/5$

Given -

$2x-y=4$ ------------------(1)
$3x-4y=7$ -----------------(2)

Solve equation (1) for $y$

$2x-y=4$
$-y=4-2x$
$y=-4+2x$

Substitute $y=-4+2x$ in equation (2)

$3x-4y=7$
$3x-4(-4+2x)=7$
$3x+16-8x=7$
$-5x=7-16=-9$
$x=(-9)/(-5)=9/5$
$x=9/5$

Substitute $x=9/5$ in eqation (1)

$2x-y=4$
$2(9/5)-y=4$
$18/5-y=4$
$-y=4-18/5$
$-y=(20-18)/5=2/5$
$y=-2/5$

How do solve the following linear system?: 2x-y=4 , 3x – 4y = 7 2x-y=4 , 3x – 4y = 7 ?