Explanation:
the solution of such a system of inequalities with 2 variables is the joined area above both lines (that are the bottom delimiters of both inequalities).
these lines are just the equations instead of the inequalities.
we have the lines
y = 4x - 3
y = -2x + 3
when going from left to right (x goes from -infinity to +infinity), the line y = -2x + 3 is first above the other line.
we know this, because the y-intercept (+3 vs. -3) is above, and the slope (-2 vs. 4) makes the line going downward from high above on the left.
at the intersection point between the 2 lines this changes, and we have to stay above y = 4x - 3.
so, we need the intersection point :
4x - 3 = -2x + 3
6x = 6
x = 1
y = 4x - 3 = 4×1 - 3 = 4 - 3 = 1
so, the solution is
y >= -2x + 3 -infinity < x <= 1 or simply x <= 1
y > 4x - 3 1 < x < +infinity or simply x > 1
it is important to maintain the original inequality type (<, >, <=, >=).
the intersection point is included, because of the ">=" sign in the second inequality.