Question

Learning Task 2.
A. Solve the systems of equations by a) graphing b) elimination c) substitution
Eq. 1: 2x - 3y = -1; Eq. 2: y * X-1
B. Solve the problem using any method.
The sum of two numbers is 32 and the difference is 2. Find the numbers​

Answer 1

Given :- A. Solve the systems of equations by a) graphing b) elimination c) substitution

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1 .

B. Solve the problem using any method.

The sum of two numbers is 32 and the difference is 2. Find the numbers .

Solution :-

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1

a.) By graphing :-

The value of x and y of the two equation is where the two line intersect.

Let x = 0 .

then,

→ 2x - 3y = -1

→ 0 - 3y = -1

→ y = 1/3

• One solution is (0 , 1/3)

Now, Let y = 0 .

then,

→ 2x - 3y = -1

→ 2x - 0 = -1

→ x = -1/2

• second solution is (-1/2,0).

Now, Graph the line 2x - 3y = -1 using (-1/2,0) and (0,1/3).

For Eq2 now, y = x - 1

Let x = 0

then,

→ y = x - 1

→ y = 0 - 1

→ y = (-1)

• One solution is (0, -1).

Now, Let y = 0.

then,

→ y = x - 1

→ 0 = x - 1

→ x = 1

• second solution is (1,0) .

Now, Graph the line using (0,-1) and (1,0).

Now, we can conclude that, the line intersect at (4,3),

Therefore x = 4 and y = 3.

b.) By Elimination Method :-

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1

→ 2x - 3y = -1

→ y = x - 1

Multiply Eq.2 by 2 we get,

→ 2y = 2(x - 1)

→ 2y = 2x - 2

→ 2x - 2y = 2 ---------- Eq(3)

Now Subtracting Eq(1) from Eq(3) we get,

→ (2x - 2y) - (2x - 3y) = 2 - (-1)

→ 2x - 2x - 2y + 3y = 2 + 1

→ y = 3 .

Putting value of y in Eq(1) now,

→ 2x - 3y = (-1)

→ 2x - 3*3 = (-1)

→ 2x - 9 = (-1)

→ 2x = (-1) + 9

→ 2x = 8

→ x = 4.

Therefore x = 4 and y = 3.

c.) By substitution Method :-

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1

→ 2x - 3y = (-1)

→ y = x - 1

Putting value of y from Eq.2 in Eq.1 , we get,

→ 2x - 3(x - 1) = (-1)

→ 2x - 3x + 3 = (-1)

→ (-x) = (-1) - 3

→ (-x) = (-4)

→ x = 4 .

then,

→ y = x - 1

→ y = 4 - 1

→ y = 3 .

Therefore x = 4 and y = 3.

Solution (B) :-

Let us assume that, the given two numbers are x and y, where x > y .

then,

→ x + y = 32 ------------ Eqn.(1)

→ x - y = 2 --------------- Eqn.(2)

By Elimination Method , adding both Eqn. we get,

→ (x + y) + (x - y) = 32 + 2

→ x + x + y - y = 34

→ 2x = 34

→ x = 17 .

Putting value of x in Eqn.(1), we get,

→ x + y = 32

→ 17 + y = 32

→ y = 32 - 17

→ y = 15 .

Therefore, Required two numbers are 15 and 17.

Learn more :-

इस एक्स इक्वल टू रूट 3 प्लस वन डिवाइडेड बाय टू फाइंड द वैल्यू ऑफ एक्स क्यूब प्लस टू एक्स स्क्वायर माइनस 8 एक्स प्लस 7

https://brainly.in/question/20858452

if a^2+ab+b^2=25

b^2+bc+c^2=49

c^2+ca+a^2=64

Then, find the value of

(a+b+c)² - 100 = ...

https://brainly.in/question/16231132

Answer 2

Answer:

Given :- A. Solve the systems of equations by a) graphing b) elimination c) substitution

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1 .

B. Solve the problem using any method.

The sum of two numbers is 32 and the difference is 2. Find the numbers .

Solution :-

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1

a.) By graphing :-

The value of x and y of the two equation is where the two line intersect.

Let x = 0 .

then,

→ 2x - 3y = -1

→ 0 - 3y = -1

→ y = 1/3

One solution is (0 , 1/3)

Now, Let y = 0 .

then,

→ 2x - 3y = -1

→ 2x - 0 = -1

→ x = -1/2

second solution is (-1/2,0).

Now, Graph the line 2x - 3y = -1 using (-1/2,0) and (0,1/3).

For Eq2 now, y = x - 1

Let x = 0

then,

→ y = x - 1

→ y = 0 - 1

→ y = (-1)

One solution is (0, -1).

Now, Let y = 0.

then,

→ y = x - 1

→ 0 = x - 1

→ x = 1

second solution is (1,0) .

Now, Graph the line using (0,-1) and (1,0).

Now, we can conclude that, the line intersect at (4,3),

Therefore x = 4 and y = 3.

b.) By Elimination Method :-

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1

→ 2x - 3y = -1

→ y = x - 1

Multiply Eq.2 by 2 we get,

→ 2y = 2(x - 1)

→ 2y = 2x - 2

→ 2x - 2y = 2 ---------- Eq(3)

Now Subtracting Eq(1) from Eq(3) we get,

→ (2x - 2y) - (2x - 3y) = 2 - (-1)

→ 2x - 2x - 2y + 3y = 2 + 1

→ y = 3 .

Putting value of y in Eq(1) now,

→ 2x - 3y = (-1)

→ 2x - 3*3 = (-1)

→ 2x - 9 = (-1)

→ 2x = (-1) + 9

→ 2x = 8

→ x = 4.

Therefore x = 4 and y = 3.

c.) By substitution Method :-

Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1

→ 2x - 3y = (-1)

→ y = x - 1

Putting value of y from Eq.2 in Eq.1 , we get,

→ 2x - 3(x - 1) = (-1)

→ 2x - 3x + 3 = (-1)

→ (-x) = (-1) - 3

→ (-x) = (-4)

→ x = 4 .

then,

→ y = x - 1

→ y = 4 - 1

→ y = 3 .

Therefore x = 4 and y = 3.

Solution (B) :-

Let us assume that, the given two numbers are x and y, where x > y .

then,

→ x + y = 32 ------------ Eqn.(1)

→ x - y = 2 --------------- Eqn.(2)

By Elimination Method , adding both Eqn. we get,

→ (x + y) + (x - y) = 32 + 2

→ x + x + y - y = 34

→ 2x = 34

→ x = 17 .

Putting value of x in Eqn.(1), we get,

→ x + y = 32

→ 17 + y = 32

→ y = 32 - 17

→ y = 15 .

Therefore, Required two numbers are 15 and 17.

Learn more :-

इस एक्स इक्वल टू रूट 3 प्लस वन डिवाइडेड बाय टू फाइंड द वैल्यू ऑफ एक्स क्यूब प्लस टू एक्स स्क्वायर माइनस 8 एक्स प्लस 7

brainly.in/question/20858452

if a^2+ab+b^2=25

b^2+bc+c^2=49

c^2+ca+a^2=64

Then, find the value of

(a+b+c)² - 100 = ...

Step-by-step explanation: