Asystem of equations consists of a line s of the equation y = x - 5 that is graphed in orange, and a line t that passes through the points (0, 2) and (8, -4). the equation of line t is y = −3
4
x + 2. what is the solution to this system of linear equations?

The solution of the system of linear equation is (4,-1) and this can be determined by using the arithmetic operations.

Given :

Equations  ---  y = x - 5   --- (1)

                           --- (2)

The system of linear equations can be determined by substituting the value of y in terms of x in another equation in order to determine the value of 'x' and by finding the value of 'x', the value of 'y' can also be determined.

Substitute the value of 'y' in equation (2) that is:

Further, simplify the above equation.

7x = 28

x = 4

Now, substitute the value of 'x' in equation (1) that is:

y = 4 - 5

y = -1

So, the solution of the system of linear equation is (4,-1).

For more information, refer to the link given below:

link

Step-by-step explanation:

Look at the picture.

Mark points (0, 2) and (8, -4) in the coordinate system.

Plot the line going through these points.

Read the coordinates of the intersection of the line (solution).