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Q: Which of these ordered triples indicates where the plane cuts the y axis for this equation 2x plus 3y plus 6z equals 54?

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There are 6 such triples.

Using the equation below, select the ordered triple that correctly indicates where the plane cuts the x-axis.3x+4y+8z=12

I am sorry but the question is incomplete. You have not mentioned the ordered pairs and the equation is incomplete as well.

13

3x

x = 5 and y = 4

x = 2 and y = -4

7x + 2y + 3z = 42At the z-axis, 'x' and 'y' are both zero.0 + 0 + 3z = 42z = 14The coordinates of the z-intercept (the 'ordered triple') are (0, 0, 14)

(0, 6)

There are an infinite number of ordered pairs that satisfy the equation.

15

There are infinitely many ordered pairs. One of these is (0, 0).

The list of choices that accompanies the question is really short.2x + 3y + 6z = 54At the y-intercept, 'x' and 'z' are zero.3y = 54y = 18

x = 12 y = 2 (12,2) satifies the equation

There are infinitely many ordered pairs: each point on the straight line defined by the equation is an ordered pair that is a solution. One example is (0.5, 2.5)

The solution set for a linear equation in two variables comprises an infinite number of ordered pairs, and these are defined by the equation that appears in the question!

1,6 2,12 3,18 4,24 5,30

(4.25, 0.25) is a solution.

7

(0, 6.5) is one option.

There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)

There are an infinite number of ordered pairs. Any point on the straight line which passes through (0,4) and has a gradient of -2 will be an ordered pair for the equation.

They are the coordinates of the infinitely many points on the line defined by the equation.

(1, 0.2), (2, 0.1)

12