Solve the pair of equation:
2/x+3/y=11,5/x-4/y=-7
And find the value of 5x-3y
Answers
Answer:
The value of 5x-3y is 4
Step-by-step explanation:
Given equations are \frac{2}{x}+\frac{3}{y}=11\hfill (1)
x
2
+
y
3
=11\hfill(1) and
\frac{5}{x}-\frac{4}{y}=-7\hfill (2)
x
5
−
y
4
=−7\hfill(2)
To find the value of 5x-3y :
First find the values of x and y :
Equation (1) becomes \frac{2}{x}+\frac{3}{y}=11\hfill (1)
x
2
+
y
3
=11\hfill(1)
2y+3x=11xy\hfill (3)2y+3x=11xy\hfill(3)
Equation (2) becomes \frac{5}{x}-\frac{4}{y}=-7\hfill (2)
x
5
−
y
4
=−7\hfill(2)
5y-4x=-7xy\hfill (4)5y−4x=−7xy\hfill(4)
Now solving the equations (3) and (4) by Elimination method
Multiply the equation (3) into 4 we get
8y+12x=44xy\hfill (5)8y+12x=44xy\hfill(5)
Multiply the equation (4) into 3 we get
15y-12x=-21xy\hfill (6)15y−12x=−21xy\hfill(6)
Now adding the equations (5) and (6) we get
8y+12x=44xy8y+12x=44xy
15y-12x=-21xy15y−12x=−21xy
___________________
23y=23xy23y=23xy
Rewritting the equation
23xy=23y23xy=23y
x=\frac{23y}{23y}x=
23y
23y
=1=1
Therefore x=1x=1
Substitute the value of x in the equation (3) we get
2y+3(1)=11(1)y2y+3(1)=11(1)y
2y+3=11y2y+3=11y
2y-11y=-32y−11y=−3
-9y=-3−9y=−3
y=\frac{3}{9}y=
9
3
Therefore y=\frac{1}{3}y=
3
1
Now to find 5x-3y
Substitute the values of x and y we get
5(1)-3(\frac{1}{3})=5-15(1)−3(
3
1
)=5−1
=4=4
Therefore 5x-3y=4