Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

Given lines are:

2x + y = 5 …(i)

x + 3y = -8 …(ii)

Firstly, we find the point of intersection of eq. (i) and (ii)

Multiply the eq. (ii) by 2, we get

2x + 6y = -16 …(iii)

On subtracting eq. (iii) from (i), we get

2x + y – 2x – 6y = 5 – (-16)

⇒ -5y = 5 + 16

⇒ -5y = 21

Putting the value of y in eq. (i), we get

⇒ 10x = 46

Hence, the point of intersection is

Now, we find the slope of the given equation 3x + 4y = 7

We know that the slope of an equation is

So, the slope of a line which is parallel to this line is also

Then the equation of the line passing through the point having slope is:

y – y₁ = m (x – x₁)

⇒ 3x + 4y + 3 = 0