To calculate: The solution for the system of equations 0.2x=0.35y−2.5 and 0.16x+0.5y=5.8, if the system...

Calculation:
Consider the provided system of equations:
${\displaystyle 0.2x=0.35y-2.5}$ and ${\displaystyle 0.16x+O.5y=5.8}$
Convert the equations into standard form ${\displaystyle Ax+By=C}$ by multiplying with 100 to clear decimals:
${\displaystyle 0.2x—0.35y=-2.5}$
${\displaystyle 20x-35y=-250}$ ............(1)
${\displaystyle 4x—7y=-50}$
And,
${\displaystyle 0.16x+0.5y=5.8}$
${\displaystyle 16x+50y=580}$ ............(2)
${\displaystyle 8x+25y=290}$
Now, multiply by —2 in equation (1):
${\displaystyle -8x+14y=100}$ ............(3)
Now, add equation (2) and (3)
${\displaystyle -8x+14y=100}$
${\displaystyle 8x+25y=100}$
$14y+25y=390$
Substitute 10 for yin equation (1) and solve for x:
${\displaystyle 4x—7\left(10\right)=-50}$
${\displaystyle 4x—70=-50}$
${\displaystyle 4x=20}$
${\displaystyle x=5}$
So, the ordered pair obtained is (5,10).
Check:
Put ${\displaystyle x=5}$ and ${\displaystyle y=10}$ in the equation ${\displaystyle 4x—7y=—50}$
$$4\left(5\right)-7\left(10\right)-50$$
$$20+70-50$$
$$-50-50$$
The results true.
Put ${\displaystyle x=5}$ and ${\displaystyle y=10}$ in the equation ${\displaystyle 8x+25y=290}$
$$8\left(5\right)+25\left(10\right)290$$
$$40+250290$$
$$290290$$
The result is true.
Therefore, the solution for the system of equations $x-\frac{2}{5}y=\frac{3}{10}$ and $5x=2y+\frac{3}{2}$ is $\{(x,y)|10x-4y=3\}$