TU=1-x,UB=4x+17,TB=-3x
assuming that U is a point between T and B, we have
TB = TU+UB, so
-3x = 1-x + 4x+17
x = -3
do with that what you will
2939
To solve the system of equations TU = 1 - x, UB = 4x + 17, and TB = -3x, we can use the method of substitution.
Step 1: Solve the first equation (TU = 1 - x) for x:
To do this, we can rearrange the equation to isolate x:
TU = 1 - x
Add x to both sides of the equation:
TU + x = 1
Rearrange the equation:
x + TU = 1
Step 2: Substitute the expression for x in the second equation (UB = 4x + 17) with x + TU from the first equation:
Replace x in the second equation with x + TU:
UB = 4(x + TU) + 17
Distribute the 4:
UB = 4x + 4TU + 17
Step 3: Substitute the expression for x in the third equation (TB = -3x) with x + TU from the first equation:
Replace x in the third equation with x + TU:
TB = -3(x + TU)
Distribute the -3:
TB = -3x - 3TU
Step 4: Rewrite the equations using the substitutions made:
The system of equations becomes:
x + TU = 1 (Equation 4)
UB = 4x + 4TU + 17 (Equation 5)
TB = -3x - 3TU (Equation 6)
Now we have a system of equations in terms of x and TU. From here, you can solve for both variables by solving the system of equations using methods such as substitution, elimination, or graphing.
It looks like you've provided three equations: TU = 1-x, UB = 4x+17, and TB = -3x. These equations represent a system of linear equations, which can be solved to find the values of x, TB, TU, and UB.
To solve this system, we'll use a method called substitution. Let's start by solving for x in one of the equations and substituting it into the other equations.
From the first equation, TU = 1-x, we can solve for x by subtracting 1 from both sides of the equation:
x = 1 - TU
Now we'll substitute this value of x into the other two equations.
Substituting x = 1 - TU into the second equation, UB = 4x + 17, gives us:
UB = 4(1 - TU) + 17
Simplifying this equation:
UB = 4 - 4TU + 17
UB = 21 - 4TU
Now let's substitute x = 1 - TU into the third equation, TB = -3x:
TB = -3(1 - TU)
TB = -3 + 3TU
We now have two new equations:
UB = 21 - 4TU
TB = -3 + 3TU
This system of equations can be solved using various methods like substitution, elimination, or matrices. However, it cannot be solved completely at this point without additional information or constraints.