Question 45914
Modify The Fraction:
{{{6x + 2z = -7/2}}}
{{{12x + 4z = -7}}}
Exchange The Equation:
{{{12x + 4z = -7}}}
{{{z = -3x - 7/4}}}
Plug:
{{{2y - 4z = 4}}}
{{{2y - 4(-3x - 7/4) = 4}}}
{{{2y + 12x + 7 = 4}}}
{{{y = -3/2 - 6x}}}
Plug:
{{{3x - 4y = -3}}}
{{{3x - 4(-3/2 - 6x) = -3}}}
{{{3x + 6 + 24x = -3}}}
{{{27x = -9}}}
{{{x = -1/3}}}
Plug:
{{{12x + 4z = -7}}}
{{{12(-1/3) + 4z = -7}}}
{{{-4 + 4z = -7}}}
{{{4z = -3}}}
{{{z = -3/4}}}
Plug:
{{{2y - 4z = 4}}}
{{{2y - 4(-3/4) = 4}}}
{{{2y + 3 = 4}}}
{{{2y = 1}}}
{{{y = 1/2}}}
(-1/3,1/2,-3/4)
Check:
{{{3x - 4y = -3}}}
{{{3(-1/3) - 4(1/2) = -3}}}
{{{-1 - 2 = -3}}} Correct
{{{6x + 2z = -7/2}}}
{{{6(-1/3) + 2(-3/4) = -7/2}}}
{{{-4/2 - 3/2 = -7/2}}} Correct
{{{2y - 4z = 4}}}
{{{2(1/2) - 4(-3/4) = 4}}}
{{{1 + 3 = 4}}} Correct