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

Step-by-step explanation:

Given the system of equation,

y = ...(1)

6x – 4y = –10 ...(2)

Substituting equation 1 into 2 we have;

6x - 4(2x/3 +2)= -10

6x -8x/3 -8 = -10

Multiplying through by 3;

18x-8x-24=-30

10x=-30+24

10x = -6

Dividing both sides by 10

10x/10 = -6/10

x = -0.6

Substituting x = -0.6 into equation 1 to get the value of y we have;

y = 2(-0.6)/3 + 2

y = -1.2/3 + 2

y = -0.4+2

y = 1.6

This shows that the linear equation has only one solution. The solution is

x = -0.6 and y = 1.6

step-by-step explanation: