Question

Find the value of x + y and xy if x + y = 5 and x - y = 3.​

Answer 1

Given

we have given x+y= 5 & x-y= 3

To find

We have to find x+y and xy

$\sf\huge \mathbb{\underline{\underline{{Solution}}}}$

➙x+y= 5-------(1)

➙x-y= 3---------(2)

Adding Equation 1 and Equation 2

➙x+y+x-y= 5+3

➙2x+y-y=8

➙2x=8

➙x=8÷2

x=4

Put X's value in Equation 1

➙x+y=5

➙4+y=5

y= 5-4=1

y=1

Check:

x+y=5

=>4+1=5

Now,we have to find x+y and xy

=> x+y = 4+1=5

x+y = 4+1=5=>xy= 4×1= 4

Alternative Method

=> x+y= 5

x= 5-y---(1)

=>x-y=3

=>(5-y)-y=3

=>5-2y=3

=>-2y= 3-5

=>-2y= -2

y=1

=>x= 5-y

=>x= 5-1=4

x+y= 4+1=5

x+y= 4+1=5xy= 4×1= 4

Answer 2

Step-by-step explanation:

Given

we have given x+y= 5 & x-y= 3

To find

We have to find x+y and xy

$\sf\huge \mathbb{\underline{\underline{{Solution}}}} </p><p>Solution</p><p>$

➙x+y= 5-------(1)

➙x-y= 3---------(2)

Adding Equation 1 and Equation 2

➙x+y+x-y= 5+3

➙2x+y-y=8

➙2x=8

➙x=8÷2

x=4

Put X's value in Equation 1

➙x+y=5

➙4+y=5

y= 5-4=1

y=1

Check:

x+y=5

=>4+1=5

Now,we have to find x+y and xy

=> x+y = 4+1=5

x+y = 4+1=5=>xy= 4×1= 4

Alternative Method

=> x+y= 5

x= 5-y---(1)

=>x-y=3

=>(5-y)-y=3

=>5-2y=3

=>-2y= 3-5

=>-2y= -2

y=1

=>x= 5-y

=>x= 5-1=4

x+y= 4+1=5

x+y= 4+1=5xy= 4×1= 4