Answer:
there is only one solution, the answer is (A) one solution -0.6,-1.6.
Explanation:
To find out how many solutions the system has, we can solve it using either substitution or elimination method. Let's use the elimination method here:
Y = (2/3)x + 2 --- equation 1
6x - 4y = -10 --- equation 2
To eliminate y, let's multiply equation 1 by 4:
4y = 8/3x + 8
Now, we can substitute this expression for 4y into equation 2 and simplify:
6x - (8/3x + 8) = -10
Multiplying both sides by 3 to get rid of the fraction:
18x - 8x - 24 = -30
Simplifying further:
10x = -6
x = -0.6
Now we can substitute x = -0.6 into either equation 1 or equation 2 to find y:
Using equation 1:
y = (2/3)(-0.6) + 2 = 1.6
Therefore, the solution to the system is (-0.6, 1.6).
Since there is only one solution, the answer is (A) one solution -0.6,-1.6.