for graph onefirst, find the lines y=3/4x-3 and y=-2x+1 remember that if we have y>something or y<something, it's a dotted line and if it's y≤something or y≥something, it's a solid line
remember for y=mx+bm=slope and b=y intercept
remember the slope=rise/run
for y=3/4x-3y intercept is -3 so start at the origin and go 3 units down the y axis and put a point thereslope is 3/4 so rise/run=3/4, from that y intercept, go up 3 units and go to the right 4 units and put another point, connect the points with a dotted line since it was < or >
we need to now know which side to shaderemeber that the shaded area is the solution area
now, for the y>3/4x-3, see if the origin is a solution or if it or not (you can pick any point but (0,0) is an easy one to use)0>3/4(0)-30>-3false, so the origin is not in the solution area, shade on the side of the line that doesn't contain the origin
for y=-2x+1y intercpet is 1 so start from the origin and go up 1 unit on the y axis and put a point thereslope is -2 or -2/1 so rise/run=-2/1, go from the y intercept, go up -2 units (or down 2 units) and right 1 unit and put another point there, connect the points with a solid line since it was ≤ or ≥
now find where to shadetest a point (I choose (0,0) )0≤-2(0)+10≤1falseso the origin is not in the shaded area, shade the area that doesn't contain the origin
we get the resulting picture attached below (I graphed with desmos)
2nd questiona.say x=number of adult tickets sold and y=number of kids tickets soldmoney made=number of tickets times cost per ticketso total money made=adultmoney+kidsmoney=adultcost*x+kidscost+y=12*x+8*y=12x+8yso moneymade=12x+8ymoneymade=808808=12x+8y12x+8y=808
sold 75 ticketsso total is 75x+y=75
our system is 12x+8y=808 andx+y=75
b. subsitutionlet's look at x+y=75solve for one varaible or get it by itselfminus y from both sides (you can do x but it doesn't matter)x=75-yso now we can put 75-y whereever you see x in the equations
replace x with 75-y12x+8y=80812(75-y)+8y=808distribute900-12y+8y=808900-4y=808minus 900 both sides-4y=-92divide both sides by -4y=23
solve for xx=75-yx=75-23x=52
c. x=52y=23
so 52 adult tickets were sold and 23 kids tickets were sold