Question

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

A) no solution
B) one solution
C) two solutions
D) infinitely many solutions

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.