Question 465399
1)

{{{ 3x - 4y = -30}}}........1

{{{-5x -2y = -22}}}.........2......both sides multiply by {{{-2}}}
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{{{-5x(-2) -2y(-2) = -22(-2)}}}.........2

{{{10x +4y = 44}}}.....2....add to 1
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{{{ 3x -4y = -30}}}........1
{{{10x +4y = 44}}}..........2
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{{{ 3x+10x -4y+4y = -30+44}}}

{{{ 13x -cross(4y)+cross(4y) = 14}}}

{{{ 13x= 14}}}

{{{ x= 14/13}}}

{{{ highlight(x= 1.08)}}}

{{{ 3x -4y = -30}}}........1.plug in {{{ x= 1.08}}}

{{{ 3(1.08) -4y = -30}}}

{{{ 3.24 +30 = 4y}}}

{{{ 33.24 = 4y}}}

{{{ y=33.24/4}}}

{{{ highlight(y=8.31)}}}


check:

{{{ 3x -4y = -30}}}........1

{{{ 3(1.08) -4(8.31) = -30}}}

{{{ 3.24 -33.24 = -30}}}

{{{ -30 = -30}}}


2) 
{{{-6x - 6y = -18}}}........1

{{{-4x - 3y = -11}}}........2.....both sides multiply by {{{-2}}}
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{{{-4x(-2) -3y(-2) = -11(-2)}}}

{{{8x +6y = 22}}}................add to 1
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{{{-6x - 6y = -18}}}........1
{{{8x +6y = 22}}}...........2
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{{{-6x +8x- 6y+6y = -18+22}}}


{{{2x= 4}}}

{{{highlight(x= 2)}}}

{{{-4*2 - 3y = -11}}}........2.

{{{-8 +11 = 3y}}}

{{{3 = 3y}}}

{{{highlight(y=1)}}}



3) 
{{{6x - 10y = 8}}}........1 .....solve for {{{x}}}

{{{5x - 6y = 16}}}..........2
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{{{6x - 10y = 8}}}........1

{{{6x = 10y + 8}}}


{{{x = 10y/6 + 8/6}}}.........substitute in 2
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{{{5(10y/6 + 8/6) - 6y = 16}}}..........2....solve for {{{y}}}

{{{5(10y+ 8)/6 - 6y = 16}}}


{{{0.833(10y+ 8) - 6y = 16}}}

{{{8.33y+ 6.664 - 6y = 16}}}

{{{2.33y = 16-6.664}}}

{{{2.33y =9.336}}}

{{{y =9.336/2.33}}}

{{{highlight(y =4.007)}}}

now find {{{x}}}

{{{x = 10y/6 + 8/6}}}

{{{x = 10(4.007)/6 + 8/6}}}

{{{x = (40.07)/6 + 8/6}}}

{{{x = 6.678 + 1.33}}}

{{{highlight(x = 8.008)}}}

{{{6x - 10y = 8}}}

4) 

{{{-5x -5y = 0}}}.....1 .....solve for {{{x}}}

{{{7x + 4y = 24 }}}...2
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{{{-5x -5y = 0}}}.....1

{{{-5x+5x -5y = 0+5x}}}

{{{-5y = 5x}}}

{{{-5y/5 = 5x/5}}}

{{{x=-y }}}.................substitute in 2
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{{{7(-y) + 4y = 24 }}}...2..solve for {{{y}}}

{{{-7y + 4y = 24 }}}

{{{-3y  = 24 }}}

{{{y  = 24/-3 }}}

{{{highlight(y  = -8) }}}


now find {{{x}}}

{{{x=-y }}}

{{{x=-(-8) }}}

{{{highlight(x=8)}}}