folklorahhe

2021-11-15

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 does not have one unique solution, state whether the system is inconsistent, or whether the equations are dependent.

Marlene Broomfield

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

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