Given:
Given that the two linear equations in the graph are [tex]y=-3x+6[/tex] and [tex]y=2x-4[/tex]
We need to determine the number of solutions can be determined from the system of linear equations.
Solutions:
The number of solutions to the system of linear equations can be determined using the substitution method.
Substituting [tex]y=-3x+6[/tex] in the equation [tex]y=2x-4[/tex], we get;
[tex]-3x+6=2x-4[/tex]
Subtracting both sides of the equation by 2x, we get;
[tex]-5x+6=-4[/tex]
Subtracting both sides of the equation by 6, we have;
[tex]-5x=-10[/tex]
Dividing both sides of the equation by -5, we get;
[tex]x=2[/tex]
Thus, the value of x is 2.
Substituting [tex]x=2[/tex] in the equation [tex]y=-3x+6[/tex], we get;
[tex]y=-3(2)+6[/tex]
[tex]y=-6+6[/tex]
[tex]y=0[/tex]
Thus, the value of y is 0.
Hence, the solution to the system of linear equations is (2,0)
Therefore, the system of equations have one solution.
Thus, Option B is the correct answer.
