Question

7x-3y=31 ও 9x-5y=41 দুইটি সরল সমীকরণ। ক) (4,-1) বিন্দুটি কোন সমীকরনকে সিদ্ধ করে? খ) প্রতিস্থাপন পদ্ধতিতে সমাধান করে (x,y) নির্ণয় কর। গ) লেখচিত্রের সাহায্য সমীকরণ জোটের সমাধান নির্ণয় কর?​

Answer 1

x = 1.9, y = -5.9

• 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.

Given system of linear equations are,

7x-3y = 31 and 9x-5y = 41.

Now, putting the point in both the equations that is putting x = 4 and y = -1 in both the equations, we get the values as,

7(4) - 3(-1) = 28 + 3 = 31.

Again, 9(4)-5(-1) = 36 + 5 = 41.

Hence, the point (4,-1) satisfies both the equations.

Now, multiplying the first equation by 5 and multiplying the second equation by 3, we get,

35x - 15y = 155 and 18x-15y = 123.

Subtracting one equation from another, we get,

17x = 32.

Or, x = 1.9

Then, y = $\frac{31-7x}{-3}$ = -5.9

Hence, x = 1.9, y = -5.9

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