graphing and wishing a answer

Question

the sum of two numbers, x andby, is less than 10. When you triple x and add it to y, the sum is less than 12

Answer 1

x+y<10

3x+y<12

find where they intersect, treat them as equalities

subtract 1st equality from the 2nd to get

2x=2, divide by 2

x=1

triple first equation and subtract the 2nd

3x+3y=30

3x +y =12

2y = 18

y= 9

graph two lines, x+y=10 and 3x+y=12 they intersect at (1,9)

shade everything below and to the left of the two lines

IF you want both x and y >0 shade in a quadrilateral with vertices

(0,0), (0,10), (1,9), and (4,0) Those are all the points that satisfy the inequalities. Make the top right sides of the quadrilateral dotted, not solid lines, to indicate the line itself is not a solution to the inequalities.