How do you solve 6x-y=-5 and 4x-2y=6?

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Answer 1 · 2015-10-08T21:56:33

$x = \frac{1}{2}$ $x=1/2$

$y = - 2$ $y=-2$

We have 2 equations and 2 unknowns so they are simultaneous.

$6 x - y = 5 (1)$ $6x-y=5 " "color(red)((1))$

$4 x - 2 y = 6 (2)$ $4x-2y=6 " "color(red)((2))$

From $(1) :$ $color(red)((1)):$

$y = (6 x - 5)$ $y=(6x-5)$

We can substitute this expression for $y$ $y$ into $(2) \Rightarrow$ $color(red)((2))rArr$

$4 x - 2 (6 x - 5) = 6$ $4x-2(6x-5)=6$

$4 x - 12 x + 10 = 6$ $4x-12x+10=6$

$- 8 x = 6 - 10$ $-8x=6-10$

$- 8 x = - 4$ $-8x=-4$

$x = \frac{- 4}{- 8} = \frac{1}{2}$ $x=(-4)/-8=1/2$

We can now substitute this value of $x$ $x$ into $(1) \Rightarrow$ $color(red)((1))rArr$

$6 \times \frac{1}{2} - y = 5$ $6xx1/2-y=5$

$3 - y = 5$ $3-y=5$

$y = 3 - 5 = - 2$ $y=3-5=-2$