Question

The expression ax + by has value 9, when x = 1, y = 2. When x = -1, y = 2, it has value 3, find a and b.

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Answer 1

Answer:

• a = 3
• b = 3

Step-by-step explanation:

Case 1: When ax + by = 9 when x = 1 and y = 2,

Substitute the value of x and y.

ax + by = 9

⇒ a(1) + b(2) = 9

⇒ a + 2b = 9 ⇢ (Equation 1)

Case 2: When ax + by = 3 when x = -1 and y = 2,

Substitute the value of x and y.

ax + by = 3

⇒ a(-1) + b(2) = 3

⇒ -a + 2b = 3 ⇢ (Equation 2)

Add Equation 1 and Equation 2.

a + 2b = 9

{+} -a + 2b = 3

4b = 12

➥ b = 12 ÷ 4

➝ b = 3

Now to find out the value of 'a', substitute the value of b in Equation 1 to find out the value of a.

a + 2b = 9

⇒ a + 2(3) = 9

⇒ a + 6 = 9

⇒ a = 3

Therefore, the value of:

• a = 3
• b = 3

Answer 2

Question given :

• The expression ax + by has value 9, when x = 1, y = 2. When x = -1, y = 2, it has value 3, find a and b.

Information provided with us:

• Value of expression ax + by = 9
• Value of x is 1
• Value of y is 2

In other condition,

• Value of x is -1
• Value of y is 2
• Result is 3

What we have to calculate:

• Values of a and b

Performing Calculations:

______________

➺ ax + by = 9

Putting the value of x and y,

➺ a(1) + b(2) = 9

➺ a×1 + b×2 = 9

➺ a + 2b = 9

➺ a = 9 - 2b

• Here we got the value of a!

Now putting the value of x as -1 and y as 2,

➺ a(-1) + b(2) = 3

➺ a × -1 + b × 2 = 3

➺ -a + 2b = 3

• Substitute the value of a we got above,

➺ -( 9 - 2b ) + 2b = 3

➺ -9 + 2b + 2b = 3

➺ -9 + 4b = 3

➺ 4b = 3 + 9

➺ 4b = 12

➺ b = 12/4

➺ b = 3

Putting the value of b in a = 9 - 2b,

• Here in this step we would get the value of a

➺ a = 9 - 2 (3)

➺ a = 9 - 2 × 3

➺ a = 9 - 6

➺ a = 3

Hence, value of a and b is 3 and 3 respectively.