How do you solve the following system?: $- \frac{1}{2} x + 5 y = - 20, y = 1 - 3 x$ $-1/2x+5y=-20 , y=1-3x$

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Answer 1 · 2016-01-10T14:07:45

Answer given in extreme detail so that you can see what is happening. With practise you should be able to do this in 4 to 5 lines.

$color(blue)(color(white)(...)(x,y) -> (1 19/31 ,3 26/31)$

Tony B

Given:
$-1/2x+5y=-20.....................................(1)$
$y=1-3x..................................................(2)$

$color(blue)("To find the value of x")$

Substitute for y in (1) using (2)

$-1/2x +5(1-3x)=-20...........................(1_a)$

Multiplying out the brackets
$-1/2 x-15x+5=-20$

Adding the x-terms
$-31/2 x+5=-20$

Collecting like terms
$-31/2x=-25$

Multiply both sides by 2
$-31x=-50$

Multiply both sides by (-1)
$31x=50$

Divide both sides by 31
$x=50/31..........................................(3)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To find the value of y")$

Substitute equation (3) into equation (2) giving

$y=1-3x -> y=1-3(50/31)$

$y=1 - 150/31$

$y=-119/31 =-3 26/31$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Putting it all together")$

The point of intersection of the two graphs/equations is:

$(x,y) -> (1 19/31 ,3 26/31)$

How do you solve the following system?: -1/2x+5y=-20 , y=1-3x −12x+5y=−20,y=1−3x-1/2x+5y=-20 , y=1-3x