Question 658968
Hi
These equations are in the slope-intercept form.
I would put them into the standard form which
looks like {{{ ax + by = c }}}
{{{ y = -6x + 30 }}}
Add {{{ 6x }}} to both sides
(1) {{{ 6x + y = 30 }}}
and
{{{ y=3x-6 }}}
Subtract {{{ y }}} from both sides
{{{ 0 = 3x - y - 6 }}}
Add {{{ 6 }}} to both sides
{{{ 6 = 3x - y }}}
Now write it the other way around
(2) {{{ 3x - y = 6 }}}
Add equations (1) and (2)
(1) {{{ 6x + y = 30 }}}
(2) {{{ 3x - y = 6 }}}
{{{ 9x = 36 }}}
{{{ x = 4 }}}
Now plug this result back into (1) or (2)
(1) {{{ 6*4 + y = 30 }}}
(1) {{{ 24 + y = 30 }}}
(1) {{{ y = 30 - 24 }}}
(1) {{{ y = 6 }}}
The intersection is at ( 4,6 )
Here's the plot:
{{{ graph( 400, 400, -4, 10, -4, 10, -6x + 30, 3x - 6 ) }}}