Question

when we think about two linear equations in two variables at the same time, they are called....​

Answer 1

Answer:

Two linear equations in two variables taken together are called simultaneous linear equations.

Step-by-step explanation:

Step I: Indentify the unknown variables; assume one of them as x and the other as y

Here two unknown quantities (variables) are:

Price of each pencil cutter = $x

Price of each pen = $y

Step II: Identify the relation between the unknown quantities.

Price of 3 pencil cutter =$3x

Price of 2 pens = $2y

Therefore, first condition gives: 3x – 2y = 2

Step III: Express the conditions of the problem in terms of x and y

Again price of 7 pencil cutters = $7x

Price of 3 pens = $3y

Therefore, second condition gives: 7x + 3y = 43

Simultaneous equations formed from the problems:

3x – 2y = 2 ----------- (i)

7x + 3y = 43 ----------- (ii)

For examples:

(i) x + y = 12 and x – y = 2 are two linear equation (simultaneous equations). If we take x = 7 and y = 5, then the two equations are satisfied, so we say (7, 5) is the solution of the given simultaneous linear equations.

(ii) Show that x = 2 and y = 1 is the solution of the system of linear equation x + y = 3and 2x + 3y = 7

Put x = 2 and y = 1 in the equation x + y = 3

L.H.S. = x + y = 2 + 1 = 3, which is equal to R.H.S.

In 2ⁿᵈ equation, 2x + 3y = 7, put x = 2 and y = 1 in L.H.S.

L.H.S. = 2x + 3y = 2 × 2 + 3 × 1 = 4 + 3 = 7, which is equal to R.H.S.

Thus, x = 2 and y = 1 is the solution of the given system of equations.