Question

Solve using the elimination method 0.3x-0.2y=4 0.4x+0.5y=1

Answer 1

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

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