Question 1153575

I can’t find the x- and y-intercepts of this equation: {{{4y + 5x = 2y - 3x + 16}}}. I have already tried finding the X intercept by replacing all of the Y coefficients in the equation with 4(0) and 2(0) and, after simplifying everything, I got: -5x= -3x+16. So I did what I thought I should have done, which was dividing -5X by -5 to isolate the variable, and did the same on the other side. But, I am not sure as to where to put the other (divided by -5). So I tried both: {{{(-5x)/-5=(-3x+16)/-5}}} and {{{(-5x)/-5=(-3x)/-5+16/-5}}}. The first one resulted in x=0.6x and the second one became x=0.6x-3.2, I think. I don’t know what to do with this, please help.
<pre>4y + 5x = 2y - 3x + 16
2y + 5x = - 3x + 16 --- Subtract 2y from each side
2y = - 8x + 16 -------- Subtract 5x from each side
2(y) = 2(- 4x + 8) ---- Factoring out GCF, 2
y = - 4x + 8
As the above is in SLOPE-INTERCEPT form (y = mx + b), we see that b, or the {{{highlight_green(matrix(1,7, y-intercept, "is:", "8,", or, "point:", "(0,", "8)"))}}}
Substituting 0 for y in the above simplified-equation gives you the x-intercept, as follows: {{{highlight_green(system(matrix(3,3, y, "=", - 4x + 8,
0, "=", - 4x + 8,
4x, "=", 8),
matrix(1,9, x, "=", 8/4, "=", "2,", or, "point:", "(2,", "0)"))))}}}