(x+y-8)÷2=(x+2y-14)÷2 (x+2y-14)÷8=(3x+y-12)÷11 Solve this equations in …

The given equations are:
{tex}\frac { x + y - 8 } { 2 } = \frac { x + 2 y - 14 } { 3 } = \frac { 3 x + y - 12 } { 11 }{/tex}
Therefore, we have
{tex}\frac { x + y - 8 } { 2 } = \frac { 3 x + y - 12 } { 11 }{/tex}
By cross multiplication,we get
{tex}11x + 11y - 88 = 6x + 2y - 24{/tex}
{tex}11x - 6x + 11y -2y = -24 + 88{/tex}
{tex}5x + 9y = 64 {/tex}..........(i)

 and {tex}\frac { x + 2 y - 14 } { 3 } = \frac { 3 x + y - 12 } { 11 }{/tex}
By cross multiplication,we get
{tex}11x + 22y -154 = 9x + 3y - 36{/tex}
{tex}11x - 9x + 22y -3y = -36 + 154{/tex}
{tex}2x + 19y = 118{/tex}.........(ii)

Multiplying (i) by 19 and (ii) by 9, we get
{tex}95x + 171y = 1216{/tex} .......(iii)
{tex}18x + 171y = 1062{/tex} .......(iv)
Subtracting (iv) from (iii),we get
{tex}77 x = 154 \Rightarrow x = 2{/tex}

Substituting x = 2 in (i),we get
{tex}5 \times 2 + 9 y = 64 \Rightarrow 9 y - 54{/tex}
{tex}\therefore{/tex} Solution is x = 2, y = 6