Question

How many solutions does this linear system have?
Y=2/3x+2
6x-4y=-10

Answer 1

Answer:

B

Step-by-step explanation:

Answer 2

Given linear system of equation $y=\frac{2}{3} x +2$ , $6x-4y =-10$ has exactly one solution.

What is system of equation?

" A system of equation is a finite set of equations for which we find a common solution."

Condition used

Linear system of equations

$a_{1} x + b_{1} + c_{1} =0\\\\a_{2} x + b_{2} + c_{2} =0$

Condition for exactly one solution

$\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }$

According to the question,

Given linear system of equation,

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

⇒ $2x-3y+6=0$                                   _____(1)

$6x-4y =-10$

⇒$6x-4y+10=0$                                 ______(2)

From (1) and (2) substitute the value in the condition of linear system of equation we get,

   $\frac{a_{1} }{a_{2} } =\frac{2}{6} \\\\\frac{b_{1} }{b_{2} }=\frac{-3}{-4}$

⇒ $\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }$

Hence , linear system of equation $y=\frac{2}{3} x +2$ , $6x-4y =-10$ has exactly one solution.

Learn more about system of equation here

https://brainly.com/question/12895249

#SPJ3