The expression ax + by has value 7 when x = 2, y = 1.

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The expression ax + by has value 7 when x = 2, y = 1. When x = – 1, y = 1, it has value 1, find a and b.

Solution:

It is given that
ax + by = 7 when x = 2 and y = 1
Substituting the values
a (2) + b (1) = 7
2a + b = 7 ….. (1)
Here
ax + by = 1 when x = – 1 and y = 1
Substituting the values
a (-1) + b (1) = 1
– a + b = 1 ….. (2)
By subtracting both the equations
– 3a = – 6
So we get
a = – 6/ – 3 = 2
Substituting the value of a in equation (1)
2 × 2 + b = 7
By further calculation
4 + b = 7
b = 7 – 4 = 3
Therefore, a = 2 and b = 3.

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