7x + 2y + 3z = 42
The plane intersects each coordinate plane, but since you are interested to know where the plane cuts y-axis, this will happen when the plane cuts xy-plane or yz-plane. So you can set z = 0, or x = 0.
So, set z = 0, then the plane will cuts the xy-plane along the line 7x + 2y = 42.
If x = 0, then the y-intercept is 42/2 = 21.
There are 6 such triples.
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
15
7
There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)
Since there are no given triplets, none of them!
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
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)
I am sorry but the question is incomplete. You have not mentioned the ordered pairs and the equation is incomplete as well.
13
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 = 5 and y = 4
x = 2 and y = -4
3x
There are an infinite number of ordered pairs that satisfy the equation.
(0, 6)