If 2x+3y=0 and 3x−4y=34, then x−y=____.
- A10
- B−10
- C2
- D−2
Solution & Step-by-step Explanation
We have a system of two linear equations:
2x+3y=0⟹x=−
2
3y
Substitute x in the second equation:
3(−
2
3y
)−4y=34
−
2
9y
−4y=34
2
−9y−8y
=34
−17y=68⟹y=−4
Now substitute y=−4 back to find x:
x=−
2
3(−4)
=
2
12
=6
Find the value of x−y:
x−y=6−(−4)=6+4=10
2x+3y=0⟹x=−
2
3y
Substitute x in the second equation:
3(−
2
3y
)−4y=34
−
2
9y
−4y=34
2
−9y−8y
=34
−17y=68⟹y=−4
Now substitute y=−4 back to find x:
x=−
2
3(−4)
=
2
12
=6
Find the value of x−y:
x−y=6−(−4)=6+4=10