Question 256815
Here are the equations:
(i) 3x – 2y – 3z = -1
(ii) {{{6x + y + 2z = 7}}}
(iii) {{{9x + 3y + 4z = 9}}}
step 1 - It may be easier to get rid of the y's first. We want to multiply by easy numbers. Multiply (ii) by 2 and add to (i) to get
(iv) 3x – 2y – 3z = -1
(v) {{{12x + 2y + 4z = 14}}}
and then
(vi) {{{15x + 1z = 13}}}
step 2 - multiply (ii) by -3 and add to (iii) to get
(vii) {{{-18x - 3y - 6z = -21}}}
(viii) {{{9x + 3y + 4z = 9}}}
and then
(ix) {{{-9x -2z = -12}}}
Now, multiply (vi) by 2 and add to (ix) to get
(x) {{{30x + 2z = 26}}}
(xi) {{{-9x - 2z = -12}}}
(xii) {{{21x = 14}}}
{{{x = 2/3}}}
Since x = 2/3, we sub that back into (x) to get
{{{z = 3}}}
Now put those both back into (i) to get
{{{y = -3}}}
So we finally have {2/3, -3, 3}