The system of equations y=-1/2x+4 and y = 2x – 1 is shown on the graph below. according to the graph, what is the solution to this system of equations?
a. (2, 3)
b. (3, 2)
c. (–1, 4)
d. (4, –1)

You can use a graphing calculator in the future

(2,3)

A

 A(2,3)

Step-by-step explanation:

To solve the system of equations;

y=-1/2x+4 and y = 2x – 1

y=-1/2x+4   (1)

y = 2x – 1 (2)

Lets substitute equation 2 in equation 1

2x - 1 =  -1/2x+4

Collect like term

(We move the x variables from the right -hand side of the equation to the right-hand side of the equation to the right-hand-side of the equation and then move the constants to the right-hand side of the equation)

2x  + 1/2x  =   4  + 1

5x/2  =  5

To get the value of x, we will multiply both-side of the equation by 2/5

5x/2  ×   2/5       =  5   ×   2/5

(On the left-hand side of the equation, the 5/2 will cancel out the 2/5 leaving us with x  and on the right-hand side of the equation 5 will cancel out 5 leaving us with 2)

x   =  2

Substitute x =2 in equation (2)

y =  2x  -  1

y =  2(2)  - 1

y =   4  -1

y =3

The solution to the system of the equations is x=2 and y=3

Therefore the answer is A(2,3)