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If the pair of equations 2x + 3y = 5 and 5x + 15

2y = k represent two coincident lines, then the
value of k is:

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Answer: Two lines are coincident when they are essentially the same line, meaning they have the same slope and y-intercept. To find the value of k that makes the two given equations coincident, we need to check if the slopes and y-intercepts are the same.

Given equations:

2x + 3y = 5

5x + 15 - 2y = k

Let's rewrite equation 2 in the standard form (Ax + By = C):

2y = 5x + 15 - k

Divide both sides by 2:

y = (5/2)x + (15 - k)/2

Now we can compare the equations to find the slope and y-intercept.

Slope (m1) of equation 1: Coefficient of x = 2

Slope (m2) of equation 2: Coefficient of x = 5/2

The slopes are not equal, so the lines are not coincident.

However, let's check the y-intercepts.

Y-intercept (b1) of equation 1: Coefficient of y = 3

Y-intercept (b2) of equation 2: Constant term = (15 - k)/2

For the lines to be coincident, the y-intercepts must be equal.

So, we equate the y-intercepts and solve for k:

3 = (15 - k)/2

Multiply both sides by 2:

6 = 15 - k

Now, isolate k:

k = 15 - 6

k = 9

Therefore, the value of k that makes the two equations represent coincident lines is k = 9.

User Bluegene
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