#### 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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