Question

How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2. X 2 6x – 4y = –10 one solution: (–0. 6, –1. 6) one solution: (–0. 6, 1. 6) no solution infinite number of solutions.

Answer 1

The system of equations provides a unique solution(one solution) at (-0.6, 1.6).

Given to us,

1. $y=\dfrac{2}{3}x+2$
2. $6x-4y=-10$

Equation 2

As we already have the value of y from equation 1, substitute its value in equation 2,

$6x-4y=-10$

$6x-4(\dfrac{2}{3}x+2)=-10$

$6x-\dfrac{8}{3}x-8=-10$

$\dfrac{6x}{1}-\dfrac{8}{3}x=-10+8$

$\dfrac{6x\times 3}{1\times 3}-\dfrac{8}{3}x=-2$

$\dfrac{18x-8x}{3}=-2$

$10x=-6$

$x=\dfrac{-6}{10} \\\\x=-0.6$

Equation 1,

$y=\dfrac{2}{3}x+2$

substitute the value of x in equation 1,

$y=\dfrac{2}{3}(\dfrac{-6}{10})+2\\\\y = \dfrac{-2}{5}+2\\\\y= \dfrac{-2+10}{5}\\\\y = \dfrac{8}{5}\\\\y=1.6$

As we can see the system of equations provides a unique solution(one solution) at (-0.6, 1.6).

Learn more about the system of equations:

brainly.com/question/12895249