Question

How many solutions can be found for the system of linear equations represented on the graph?

Answer 1

Given:

Given that the two linear equations in the graph are $y=-3x+6$ and $y=2x-4$

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 $y=-3x+6$ in the equation $y=2x-4$, we get;

$-3x+6=2x-4$

Subtracting both sides of the equation by 2x, we get;

$-5x+6=-4$

Subtracting both sides of the equation by 6, we have;

$-5x=-10$

Dividing both sides of the equation by -5, we get;

$x=2$

Thus, the value of x is 2.

Substituting $x=2$ in the equation $y=-3x+6$, we get;

$y=-3(2)+6$

$y=-6+6$

$y=0$

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.