a student has two test scores in a psychology class. The mean of these scores is 76 and their range is 28. Use this information to determine the two scores. ( write a system of linear equations to solve the problem)

(x+y)/2 = 76

x-y = 28

x = 28+y

Substitute 28+y for x in first equation and solve for y. Insert that value into the second equation and solve for x. Check by inserting both values into the first equation.

To solve this problem, we'll use a system of linear equations. Let's denote the two test scores as x and y.

Given that the mean of the scores is 76, we know that the sum of the two scores is 76 multiplied by 2, which is 152. So our first equation is:
x + y = 152 ---- (Equation 1)

Given that the range of the scores is 28, we know that the difference between the two scores is 28. So our second equation is:
|x - y| = 28

Now, we can rewrite the second equation as two separate equations:
x - y = 28 ---- (Equation 2)
or
y - x = 28 ---- (Equation 3)

So, the system of linear equations is:
x + y = 152 ---- (Equation 1)
x - y = 28 ---- (Equation 2)
y - x = 28 ---- (Equation 3)

To solve this system, we can use the method of elimination or substitution. Let's use the elimination method.

Add Equation 2 and Equation 3:
(x - y) + (y - x) = 28 + 28
2x = 56
Divide both sides by 2:
x = 28

Now, substitute the value of x into Equation 1:
28 + y = 152
Subtract 28 from both sides:
y = 152 - 28
y = 124

So, the two test scores are x = 28 and y = 124.