Question 260874
Here is the original system:
(i) {{{2p + 3q =18}}}
(ii) {{{5p - q =11}}}
step 1 - I see that q's will be easier to get rid of, so I will multiply (ii) by 3 to get
(iii) {{{15p - 3q = 33}}}
step 2 - now, by adding down with (i) and (iii) , the q's are gone and I can solve for p. We get
(iv) {{{17p = 51}}}
step 3 - divide by 17 to get
(v) {{{p = 3}}}
step 4- now that we have p, we can substitute 3 for p into any equation. Let's put it into (i) and get
{{{2*3 + 3q = 18}}}
we get
{{{6 + 3q = 18}}}
subtract 6 to get
{{{3q = 12}}}
divide by 3 to get
{{{q = 4}}}
so our answer is
p = 3, q = 4.