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
x = 5 and y = 4
x = 2 and y = -4
3x
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
(0, 6)
There are an infinite number of ordered pairs that satisfy the equation.