What point P do the three planes 7x+35y+132z = 1     1x+6y+23z=1   1x+5y+19z=1intersect at?

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to find the point of intersection of the given lines, hence, you need to solve for x,y,z the system of equations, such that:

`{(7x+35y+132z = 1),(x+6y+23z = 1),(x+5y+19z = 1):}`

Elimination of one variable is one method you may approach when evaluate the system, such that:

`x + 6y + 23z - x - 5y - 19z = 1 - 1`

`y + 4z = 0`

`7x + 35y + 132z - 7x - 42y - 161z = 1 - 7`

`-7y - 29z = -6 => 7y + 29z = 6`

You may solve the new system of equations using substitution, such that:

`{(y = -4z),(7*(-4z) + 29z = 6):} => {(y = -24),(z = 6):}`

Replacing -24 for y and 6 for z in `x+5y+19z = 1` yields:

`x = 1 - 5*(-24) - 19*6 => x = 1 + 120 - 114 => x = 7`

Hence, evaluating the coordinates of point of intersection of the given lines, yields that they intersect at `x = 7, y = -24, z = 6.`

We’ve answered 318,908 questions. We can answer yours, too.

Ask a question