Question

In the xy-plane, the equations x + 2y = 10 and

Answer 1

By solving given equations, the value of c is 30.

Given two equations

x + 2y = 10 and

3x + 6y = c

These lines represents the same line for some constant c.

Value of c:

x + 2y = 10-------------(1)

3x + 6y = c-------------(2)

Dividing equation (2) by 3

$\frac{3x}{3}+ \frac{6y}{3} =\frac{c}{3}$

After solving the above equation, we get

x + 2y = c/3-----------(3)

Remember that a line is written as ax + by = c, in our case, both lines have a =1 and b = 2. Therefore, in orther that the two lines are equal, we need that, 10 = c/3

c = 10 × 3 = 30

c = 30

Therefore,

The value of c is 30.

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