To calculate: The solution for the system of equations 0.2x=0.35y-2

folklorahhe 2021-11-15 Answered
To calculate: The solution for the system of equations 0.2x=0.35y2.5 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.
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Expert Answer

Marlene Broomfield
Answered 2021-11-16 Author has 15 answers

Calculation:
Consider the provided system of equations:
0.2x=0.35y2.5 and 0.16x+O.5y=5.8
Convert the equations into standard form Ax+By=C by multiplying with 100 to clear decimals:
0.2x0.35y=2.5
20x35y=250 ............(1)
4x7y=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:
4x7(10)=50
4x70=50
4x=20
x=5
So, the ordered pair obtained is (5,10).
Check:
Put x=5 and y=10 in the equation 4x7y=50
4(5)7(10)50
20+7050
5050
The results true.
Put x=5 and y=10 in the equation 8x+25y=290
8(5)+25(10)290
40+250290
290290
The result is true.
Therefore, the solution for the system of equations x25y=310 and 5x=2y+32 is {(x,y)|10x4y=3}

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