Question

Solve: 35x + 23y = 209 and 23x + 35y = 197

Answer 1

Answer:

23x + 35y = 197 ………………(1)

35x + 23y = 209  ………………(2)

Adding eqn 1and 2

We get,

58x + 58y = 406

58( x + y) = 406

x + y = 406/58

x + y = 7   -------------- (3)

now,

23x + 35y = 197

35x + 23y = 209

On subtraction, we get

-12x + 12y = 12

12 ( -x + y) = 12

-x + y = 12/12

-x + y = 1  ------------ (4)

Now taking (3) and (4)

 x + y = 7    

-x + y = 1

Adding these , we get

2y = 8

Y = 8/2

Y = 4

Put the value of y in eqn (3)

X + 4 = 7

X = 7 – 4

x = 3

 x = 3 and y = 4.

Answer 2

x = 4 and y = 3.

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
• Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here, according to the given information, we are given that,

$35x + 23y = 209$ and $23x + 35y = 197$.

Now, Multiplying the first equation with 23 and the second equation with 35 and finding the difference between the resulting equations, we get,

$23(35x + 23y) = 23. 209$

$35(23x + 35y) = 35.197$

Then, we get,

$529y-1225y = -2088$

Or, y = 3.

Then, putting the value of x in the first equation, we get,

x = $\frac{209-69}{35} =4$.

Hence, x = 4 and y = 3.

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