Question

if

x + y = 10

x - y = 4
Then,
Find x^2 + y^2

Answer 1

Answer:

hope it helps you have a nice day

Answer 2

Answer:

$\bf{x^2+y^2 = 58}$

Step-by-step explanation:

Question:

If x+y = 10 and x-y = 4, find the value of $\bf{x^2+y^2}$

★ Concept:

Here, the concept of linear equation in two variable is used. I am going to find the value of x and y through substitution method.

Let's solve it!

Let:

• x+y = 10 be Equation (1)

• x-y = 4 be Equation (2)

Now, in Equation (2),

$\bf{x-y = 4}\\\\\implies\bf{-y=4-x}\\\\\implies\bf{y = x-4}$

Substitute the value of y in Equation (1):

$\bf{x + y = 10} \\\\\implies\bf{x+x-4 = 10}\\\\\implies\bf{2x = 14}\\\\\implies\bf{x = \dfrac{14}{2}}\\\\\implies\boxed{\bf{x=7}}$

Substitute the value of x = 7 in any equation:

$\bf{x+y = 10} \\ \\ \implies\bf{7+y = 10} \\ \\ \implies\boxed{\bf{y = 3}}$

• x = 7
• y = 3

Now,

$\bf{x^2+y^2}$

$\implies\bf{7^2+3^2}$

$\implies\bf{49+9}$

$\implies\bf{58}$

$\therefore\bf{x^2+y^2 = 58}$

★ Know More:

There are three methods to solve linear equations in two variables. They are:

• Substitution method
• Elimination Method
• Cross Multiplication Method