Question 181023
Solve the system of equations using substitution.
6x + y = 11
-6x -8y = -14
:
Use the 1st equation as the substitute, subtract 6x from both sides:
y = -6x + 11
:
Substitute (-6x+11) for y in the 2nd equation:
-6x - 8(-6x + 11) = -14
Multiply what's inside brackets, neg changes the signs:
-6x + 48x - 88 = -14
42x = -14 + 88; added 88 to both sides
42x = 74
x = {{{74/42}}}
reduces to:
x = {{{37/21}}}
:
Find y:
y = -6x + 11
y = -6({{{37/21}}}) + 11
y = {{{-222/21}}} + {{{231/21}}}
y = {{{9/21}}}
reduces to
y = {{{3/7}}}
:
:
Check solution it 2nd equation:
-6x - 8y = -14
-6({{{37/21}}}) - 8({{{3/7}}}) = 
-6({{{37/21}}}) - 8({{{9/21}}}) = 
{{{-222/21}}} - {{{72/21}}} = 
{{{-294/21}}} = -14, confirms our solution
:
I thought you could see the ordered pair is: {{{37/21}}}, {{{3/7}}}
No mention of a graph however if you graph these equations:
y = -6x + 11
and
-6x -8y = -14
6x + 8y = 14; multiply equation by -1
8y = -6x + 14
y = -.75x + {{{14/8}}}
{{{ graph( 300, 200, -2, 4, -4, 4, -6x+11,-.75x+(14/8)) }}}