Question

Solve using the elimination method

0.3x-0.2y=4

0.4x+0.5y=1

Answer 1

`\left\{\begin{array}{ccc}0.3x-0.2y=4&|\text{multiply both sides by 10}\\0.4x+0.5y=1&|\text{multiply both sides by 10}\end{array}\right\\\\\left\{\begin{array}{ccc}3x-2y=40&|\text{multiply both sides by 5}\\4x+5y=10&|\text{multiply both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}15x-10y=200\\8x+10y=20\end{array}\right}\qquad|\text{add both sides of equations}\\.\qquad23x=220\ \ \ \ |\text{divide both sides by 23}\\.\qquad\ x=(220)/(23)`

`\text{put the value of x to the second equation}\\\\4\cdot(220)/(23)+5y=10\\\\(880)/(23)+5y=10\\\\(880)/(23)+5y=(230)/(23)\ \ \ \ |\text{subtract}\ (880)/(23)\ \text{from both sides}\\\\5y=-(650)/(23)\ \ \ \ \ |\text{divide both sides by 5}\\\\y=-(130)/(23)\\\\Answer:\ x=(220)/(23),\ y=-(130)/(23)`