Question 385955
{{{3/4}}}x + 2y + {{{2/3}}}z = -3
{{{-4/5}}}y - {{{4/3}}}z = 1
z = 3
:
Replace z with 3 in the 1st two equations
{{{3/4}}}x + 2y + {{{2/3}}}(3) = -3
{{{-4/5}}}y - {{{4/3}}}(3) = 1 
Fortunately, this will cause two of fractions to cancel out
{{{3/4}}}x + 2y + 2 = -3
{{{-4/5}}}y - 4 = 1 
:
{{{3/4}}}x + 2y = -3 -2
{{{-4/5}}}y = 1 + 4
:
{{{3/4}}}x + 2y = -5
{{{-4/5}}}y = +5
:
Multiply the above equation by -5, get rid of the denominator change the signs, results:
4y = -5(5)
y = {{{(-25)/4}}}
y = -6.25
:
Find x, substitute for y and z
{{{3/4}}}x + 2y + {{{2/3}}}z = -3
y=-6.25, z=3
{{{3/4}}}x + 2(-6.25) + {{{2/3}}}(3) = -3
{{{3/4}}}x -12.5 + 2 = -3
{{{3/4}}}x -10.5 = - 3
{{{3/4}}}x = -3 + 10.5
{{{3/4}}}x = 7.5
Multiply by 4
3x = 4(7.5)
3x = 30
x = 10
:
Summarize: x=10; y=-6.25, z=3