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.

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Marlene Broomfield · Accepted Answer

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(10)=−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(5)−7(10)−50 20+70−50 −50−50 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 x−25y=310 and 5x=2y+32 is {(x,y)|10x−4y=3}

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

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