t=2x-y+5
t=y-2z+10
t=2z-2x+6
Based on the system of equations above, what is the value of t?
I get
2x = y+2
2z = x+1
so, t=7
Wait how do you get that first part?
To find the value of t, we can solve the system of equations by adding or subtracting the equations together to eliminate variables.
Let's start by adding the first and third equations:
t = 2x - y + 5 (Equation 1)
t = 2z - 2x + 6 (Equation 3)
When we add these two equations together, the x term will cancel out:
2t = (2x - 2x) + (2z - y) + (5 + 6)
2t = 0 + (2z - y) + 11
2t = 2z - y + 11
Now, let's add the second equation:
2t = 2z - y + 11 (Combined Equation 1)
Now we have eliminated the x variable. We can continue by subtracting the second equation from the combined equation:
2t - (y - 2z + 10) = 0
When we simplify this equation, we get:
2t - y + 2z -10 = 0
Finally, let's isolate the t term by rearranging the equation:
2t = y - 2z + 10
Divide both sides of the equation by 2:
t = (y - 2z + 10) / 2
Therefore, based on the system of equations given, the value of t is (y - 2z + 10) divided by 2.