What's the intercepts for the equation 4x-6y-5z=60?

1 answer:

5 0

To find the $x_i$ intercept, set $x_j=x_k=0$ . By this I refer to the following procedure.

x-intercept: Set $y=z=0$ , then you're left with $4x=60\iff x=15$ . Then the x-intercept is $(15,0,0)$ .

y-intercept: Set $x=z=0$ , then $-6y=60\iff y=-10$ . The y-intercept is $(0,-10,0)$ .

z-intercept: Set $x=y=0$ , then $-5z=60\iff z=-12$ . The z-intercept is $(0,0,-12)$ .

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Solve this system of linear equations. separate the x- and y- values with a coma. -12x=-75-11y

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Solve the following system:
{-12 x = -11 y - 75 | (equation 1)
{-5 x = -11 y - 89 | (equation 2)
Express the system in standard form:
{-(12 x) + 11 y = -75 | (equation 1)
{-(5 x) + 11 y = -89 | (equation 2)
Subtract 5/12 × (equation 1) from equation 2:
{-(12 x) + 11 y = -75 | (equation 1)
{0 x+(77 y)/12 = (-231)/4 | (equation 2)
Multiply equation 2 by 12/77:
{-(12 x) + 11 y = -75 | (equation 1)
{0 x+y = -9 | (equation 2)
Subtract 11 × (equation 2) from equation 1:
{-(12 x)+0 y = 24 | (equation 1)
{0 x+y = -9 | (equation 2)

Divide equation 1 by -12:
{x+0 y = -2 | (equation 1)
{0 x+y = -9 | (equation 2)
Collect results:
Answer: {x = -2 {y = -9

please note that the parentheses "{" should span over both equations but the editor doesn't allow that so I should it on both line, See attached example.