Question 961539
1.{{{ax+by=c}}}
2.{{{dx+ey=f}}}
From eq. 1,
{{{ax=c-by}}}
{{{x=c/a-(b/a)y}}}
Substitute into eq. 2,
{{{d(c/a-(b/a)y)+ey=f}}}
{{{(dc)/a-((db)/a)y+ey=f}}}
{{{y(e-(db)/a)=f-(dc)/a}}}
{{{y=(f-(dc)/a)/(e-(db)/a)}}}
{{{highlight(y=(af-dc)/(ae-db))}}}
Then,
{{{x=c/a-(b/a)((af-dc)/(ae-db))}}}
{{{ax=c((ae-db)/(ae-db))-b((af-dc)/(ae-db))}}}
{{{ax=(aec-dbc)/(ae-db)-(abf-dbc)/(ae-db)}}}
{{{ax=(aec-dbc-abf+dbc)/(ae-db)}}}
{{{ax=(aec-abf)/(ae-db)}}}
{{{highlight(x=(ec-bf)/(ae-db))}}}