BD= BC+CD
BC=5x+7
CD=3y+4
BD = 5x+7+3y+4
Combine alike terms:
BD = 5x+3y+11
Now, we also have that:
BD= 38
BD =2x+8y
SO:
38=5x+3y+11
2x+8y=5x+3y+11
We have a system of equations with 2 variables:
Let's rearrange them:
5x+3y+11=38
5x+3y =38-11
5x+3y=27
2x+8y=5x+3y+11
2x-5x+8y-3y=11
-3x+5y=11
Now we have:
5x+3y=27
-3x+5y=11
Solve the first for x:
5x+3y=27
5x=27-3y
x=(27-3y)/5
x= 27/5-3/5y
Replace on the second:
-3 (27/5-3/5y) +5y =11
-81/5+9/5y +5y =11
34/5y =11+81/5
34/5y = 136/5
y= 136/5 / (34/5)
y=4
Replace y=4 in the first equation:
5x+3y=27
5x+3(4)=27
Solve for x:
5x+12=27
5x=27-12
5x= 15
x=15/5
x=3
y=4, x=3