Solve the system by finding x, y, and z.

x-y+z=1
x+y+3z=-3
2x-y+2z=0

The solution is

Step-by-step explanation:

Given:

The system of equations given are:

Add first and second equations. This gives,

Adding equations 2 and 3, we get

We need solve equations 4 and 5.

Multiplying equation (4) by -3, we get

Adding the above equation to equation (5), we get

Now, we plug in in equation (4). This gives,

Now, we plug in in equation (1). This gives,

Therefore, the solution is

108 student tickets, and 176 adult tickets  were sold

Step-by-step explanation:

Adult ticket $8  Call the number of adult tickets sold "a"

Student ticket $5  Call the number of student tickets sold "s"

Since we are talking about TWO consecutive days of sold out seats, the total number of seats sold were 2* 142 = 284

Then we create two different equations with the information given:

a + s = 284

8 * a + 5 * s = 1948

we can solve for s in the first equation as follows: s = 284 - a

and use it in the second equation

8 a + 5 (284 - a) = 1948

8 a + 1420 - 5 a = 1948

combining

3 a = 528

a = 528/3

a = 176

we find the number of student tickets using this answer in the substitution equation we used:

s - 284 - 176 = 108

Therefore 108 student tickets, and 176 adult tickets  were sold.