Question

Please help me quick!!

Which of the following coordinate points is the point of intersection of these two lines?

y-6x=-4

y-2x=8


A. (12/8,11)

B. (3,14)

C. (9/6,5)

D. (-1/2,7)

Answer 1

Answer:

The point of intersection of these two lines will be: (3, 14)

Step-by-step explanation:

• The solution of two lines is the point of intersection.

Given the equations

$y-6x=-4$

$y-2x=8$

Solving the system of the equations

$\begin{bmatrix}y-6x=-4\\ y-2x=8\end{bmatrix}$

$\mathrm{Isolate}\:y\:\mathrm{for}\:y-6x=-4:\quad y=-4+6x$

$\mathrm{Subsititute\:}y=-4+6x$

$\begin{bmatrix}-4+6x-2x=8\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:-4+6x-2x=8$

$-4+6x-2x=8$

$4x=12$

$\frac{4x}{4}=\frac{12}{4}$

$x=3$

$\mathrm{For\:}y=-4+6x$

$\mathrm{Subsititute\:}x=3$

$y=-4+6\cdot \:3$

$y=14$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=3,\:y=14$

Therefore, the point of intersection of these two lines will be: (3, 14)