Rre25. find an equation involving g, h, and k that makes this augmented matrix correspond to a consistent system: 2 4 1 4 7 g 0 3 5 h 2 5 9 k 3

Multiply the first row by -g/2 and add to the second row. The new second row is

... [0, -2g, 3-g/2, 5-2g, h-7g/2]

Multiply the first row by -1 and add to the third row. The new third row is

... [0, 1, 8, k-4, -4]

Now, multiply the new second row by 1/(2g) and add to the third row. The new third row is ...

... [0, 0, 8+(3-g/2)/(2g), k-4+(5-2g)/(2g), -4+(h-7g/2)/(2g)]

This third row simplifies to

... [0, 0, (6+31g)/4g, (5-10g+2gk)/(2g), (2h-23g)/(4g)]

Normalizing each row so its pivot element is 1 and finishing the row operations necessary to leave the left three columns a diagonal matrix puts terms in the right two columns that have 6+31g in their denominator.

The equations necessary to make the system consistent appear to be

... g ≠ 0

... 6 + 31g ≠ 0

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

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step-by-step explanation:

i hope this : )