Answer is x=1.9 and y=1.7 or point (1.9,1.7)
Explanation?: Rewrite the equation for the line in slope-intercept form:
y=3x-4
The slope of this line is m = 3.
A line perpendicular to this line passing through point A(-2,3) has a slope m= -1/3.
The y-intercept for this perpendicular line [go down 2/3 and over 2 from A(-2,3) which is calculated from the slope to get to x-0] is (-2,3) + (2,-2/3) = (0,2 1/3), so b = 2 1/3.
The equation for this perpendicular line is
y=(-1/3)x+2 1/3 or
x+3y=7
Solving the system of two linear equations with two unknows substituting y=3x-4 into this equation::
x+3(3x-4)=7
Solve for x:
10x-12=7
x=19/10
19/10 + 3y = 7
30y=70-19
y = 51/30
check:
51/30 =? 3(19/10) - 4
51/30=?57/10-40/10
17/10=17/10