Answer:
The system has one solution
Step-by-step explanation:
we have the system of equations
[tex]y=\frac{2}{3}x+2[/tex] ----> equation A
[tex]6x-4y=-10[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]6x-4(\frac{2}{3}x+2)=-10[/tex]
[tex]6x-\frac{8}{3}x-8=-10[/tex]
Solve for x
Multiply by 3 both sides to remove the fraction
[tex]18x-8x-24=-30[/tex]
Combine like terms
[tex]10x=-30+24[/tex]
[tex]10x=-6[/tex]
[tex]x=-\frac{6}{10}[/tex]
Simplify
[tex]x=-\frac{3}{5}[/tex]
Find the value of y
[tex]y=\frac{2}{3}(-\frac{3}{5})+2[/tex]
[tex]y=-\frac{6}{15}+2[/tex]
[tex]y=\frac{24}{15}[/tex]
Simplify
[tex]y=\frac{8}{5}[/tex]
The solution of the system is the point [tex](-\frac{3}{5},\frac{8}{5})[/tex]
therefore
The system has one solution
