Question 923081
Elimination/Addition

{{{p+3q=16}}}.......eq.1
{{{p+q=6 }}}.........eq.2
____________subtract 2 from 1

{{{p+3q-(p+q)=16-6}}}

{{{cross(p)+3q-cross(p)-q=10}}}

{{{3q-q=10}}}

{{{2q=10}}}

{{{highlight(q=5)}}}

go to {{{p+q=6 }}}.........eq.2, plug in {{{5}}} for {{{q}}}

{{{p+5=6 }}}

{{{p=6-5 }}}

{{{highlight(p=1) }}}


by SUBSTITUTION

{{{p+3q=16}}}.......eq.1
{{{p+q=6 }}}.........eq.2
____________

{{{p+3q=16}}}.......eq.1..solve for {{{p}}}

{{{p=16-3q}}}...substitute in 2 


{{{16-3q+q=6 }}}.........eq.2..solve for {{{q}}}

{{{-2q=6-16 }}}

{{{-2q=-10 }}} ...both sides multiply by {{{-1}}}

{{{2q=10 }}}

{{{highlight(q=5) }}}....substitute in eq.1


{{{p+3*5=16}}}.......eq.1

{{{p+15=16}}}

{{{p=16-15}}}

{{{highlight(p=1)}}}


by Graphing

In order to graph these equations, we need to solve for q for each equation.

{{{p+3q=16}}}.......eq.1
{{{p+q=6 }}}.........eq.2
____________


{{{3q=-p+16}}}.......eq.1
{{{q=-p+6 }}}.........eq.2
____________

{{{q=-(1/3)p+16/3}}}.......eq.1
{{{q=-p+6 }}}.........eq.2
____________


now find two points that lie on each line

{{{q=-(1/3)p+16/3}}}.......eq.1...set {{{q=0}}}

{{{0=-(1/3)p+16/3}}}...solve for {{{p}}}

{{{(1/3)p=16/3}}}

{{{p/3=16/3}}}...if denominator same, numerator must be same too

{{{p=16}}}

point is ({{{16}}},{{{0}}})=> x(or p)-intercept

{{{q=-(1/3)p+16/3}}}.......eq.1...set {{{p=0}}}

{{{q=-(1/3)0+16/3}}}...solve for {{{p}}}

{{{q=16/3}}}

point is ({{{0}}},{{{16/3}}})=> y(or q)-intercept



{{{q=-p+6 }}}.........eq.2

{{{q=-p+6}}}.......eq.2...set {{{q=0}}}

{{{0=-p+6}}}...solve for {{{p}}}

{{{p=6}}}

point is ({{{6}}},{{{0}}})=> x(or p)-intercept


{{{q=-p+6}}}.......eq.2...set {{{p=0}}}

{{{q=0+6}}}...solve for {{{p}}}

{{{q=6}}}

point is ({{{0}}},{{{6}}})=> y(or q)-intercept


plot  points ({{{16}}},{{{0}}}) and ({{{0}}},{{{16/3}}}) and draw a line {{{q=-(1/3)p+16/3}}}

plot  points ({{{6}}},{{{0}}}) and ({{{0}}},{{{6}}})and draw a line {{{q=-p+6}}}

{{{drawing( 600, 600, -20,20, -20, 20,circle(1,5,.3),locate(1.5,6.3,p(1,5)), graph( 600, 600, -20,20, -20, 20, -x+6,-(1/3)x+16/3)) }}}