Solve the system of equations:−1x+1y=−8−2x+9y=−3Solve the system of equations:−1𝑥+1𝑦=−8−2𝑥+9𝑦=−3 a) Find Determinant D:a) Find Determinant 𝐷: Answer for part 1Answer for part 2 = Answer for part 3Answer for part 4Answer for part 5b) Find Dx:b) Find 𝐷𝑥: Answer for part 6Answer for part 7 = Answer for part 8Answer for part 9Answer for part 10c) Find Dy:
Question
Solve the system of equations:−1x+1y=−8−2x+9y=−3Solve the system of equations:−1𝑥+1𝑦=−8−2𝑥+9𝑦=−3 a) Find Determinant D:a) Find Determinant 𝐷: Answer for part 1Answer for part 2 = Answer for part 3Answer for part 4Answer for part 5b) Find Dx:b) Find 𝐷𝑥: Answer for part 6Answer for part 7 = Answer for part 8Answer for part 9Answer for part 10c) Find Dy:
Solution
The system of equations is:
-1x + 1y = -8 -2x + 9y = -3
a) To find the determinant D, we use the coefficients of x and y in the system of equations.
D = (coefficient of x in first equation * coefficient of y in second equation) - (coefficient of y in first equation * coefficient of x in second equation)
D = (-1 * 9) - (1 * -2) = -9 - (-2) = -7
b) To find Dx, we replace the coefficients of x in the determinant with the constants on the right side of the equations.
Dx = (constant in first equation * coefficient of y in second equation) - (coefficient of y in first equation * constant in second equation)
Dx = (-8 * 9) - (1 * -3) = -72 - (-3) = -69
c) To find Dy, we replace the coefficients of y in the determinant with the constants on the right side of the equations.
Dy = (coefficient of x in first equation * constant in second equation) - (constant in first equation * coefficient of x in second equation)
Dy = (-1 * -3) - (-8 * -2) = 3 - 16 = -13
The solutions to the system of equations are then x = Dx/D = -69/-7 = 9.857 and y = Dy/D = -13/-7 = 1.857.
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