Find the equation of a straight line passing through the point of
intersection of the lines
y = 2x +3 and x +y = 3 and
parallel to the line y = -5x +7

y = -5x + 3.

Step-by-step explanation:

We can find the point of intersection by solving the system:

y = 2x + 3    1

x + y = 3    2          from this:

y = 3 - x   .3

Equating equations 1 and 3:

2x + 3 = 3 - x

3x = 0

x = 0 so y = 2(0) + 3 = 3.

So the point of intersection is (0, 3).

So the required equation has slope -5 and passes through (0, 3) and,  using the point-slope form of a straight line, we have:

y - 3 = -5(x - 0)

y - 3 = -5x

y = -5x + 3.