Question

Solve the Equation
12x-14y=-8
-8x-14y=-52

Answer 1

`\large\boxed{x=(11)/(2),\ y=(86)/(35)}`

Explanation:

`\left\{\begin{array}{ccc}12x-14y=-8\\-8x-14y=-52&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}12x-14y=-8\\8x+14y=52\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad20x=44\qquad\text{divide both sides by 20}\\.\qquad x=(44:4)/(20:4)\\\\.\qquad x=(11)/(5)\\\\.\qquad\boxed{x=2.2}\\\\\text{Put the value of x to the second equation}\ 8x+14y=52:`

`8(2.2)+14y=52\\17.6+14y=52\qquad\text{subtract 17.6 from both sides}\\14y=34.4\qquad\text{divide both sides by 14}\\y=(34.4:2)/(14:2)\\\\y=(17.2\cdot10)/(7\cdot10)\\\\y=(172:2)/(70:2)\\\boxed{y=(86)/(35)}`