If EF=2x-19, FG=3x-15, and EG=26, find the values of x, EF, And FG
To find the values of x, EF, and FG, we can use the given information and solve the system of equations.
1. Start by setting up the equations using the given information:
EF = 2x - 19 (equation 1)
FG = 3x - 15 (equation 2)
EG = 26
2. We know that EG is the sum of EF and FG. So, we can set up an equation using equation 1 and equation 2:
EF + FG = EG
Substitute the values of EF and FG from equation 1 and equation 2 into the above equation:
(2x - 19) + (3x - 15) = 26
3. Simplify the equation and solve for x:
2x - 19 + 3x - 15 = 26
5x - 34 = 26
5x = 26 + 34
5x = 60
x = 60/5
x = 12
4. Now that we have found the value of x, we can substitute it back into equation 1 and equation 2 to find EF and FG:
EF = 2x - 19
= 2(12) - 19
= 24 - 19
= 5
FG = 3x - 15
= 3(12) -15
= 36 - 15
= 21
Therefore, the values of x, EF, and FG are:
x = 12
EF = 5
FG = 21