Solve by elimination and substitution
color(blue)(-x-7y=14−x−7y=14
color(blue)(x-2y=8x−2y=8
We can eliminate xx in the first equation by -x−x in the second equation
Add both the equations
rarr(-x-7y=14)+(x-2y=8)→(−x−7y=14)+(x−2y=8)
rarr-9y=22→−9y=22
color(green)(rArry=-22/9⇒y=−229
Substitute the value of yy to the second equation
rarrx-2(-22/9)=8→x−2(−229)=8
rarrx+44/9=8→x+449=8
color(green)(rArrx=8-44/9=28/9⇒x=8−449=289
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Check (-x-7y=14−x−7y=14)
rarr-28/9-7(-22/9)=14→−289−7(−229)=14
rarr-28/9+154/9=14→−289+1549=14
rarr(-28+154)/9=14→−28+1549=14
rarr126/9=14→1269=14
color(orange)(rArr14=14⇒14=14
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Check (x-2y=8x−2y=8)
rarr28/9-2(-22/9)=8→289−2(−229)=8
rarr28/9+44/9=8→289+449=8
rarr(28+44)/9=8→28+449=8
rarr72/9=8→729=8
color(violet)(rArr8=8⇒8=8
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:. color(blue)( ul bar |(x,y)=28/9,-22/9|
