Louis bought a burger and soda for $8. kate purchased a slice of pizza and soda for $9. david purchased a burger, a slice of pizza, and a soda for $13.50. write equations for each purchase. solve your equations to find the cost of a burger, slice of pizza and a soda.

cost of a burger= $4.5

Cost of soda = $3.5

Cost of a slice of pizza = $5.5

Step-by-step explanation:

Let x = the cost of a burger.

Let y = the cost of a soda.

Let z = the cost of a slice of pizza.

Louis bought a burger and soda for $8. This means

x + y = 8 - - - - - - - -1

Kate purchased a slice of pizza and soda for $9. This means

z + y = 9 - - - - - - - - - 2

David purchased a burger, a slice of pizza, and a soda for $13.50. This means

x + y + z = $13.50 - - - - - - - 3

Substituting x = 8-y and z = 9-y in equation 3, it becomes

8-y + y + 9-y = 13.50

-y -y + y = 13.50 -8-9

-y = -3.5

y = $3.5

Put y = 3.5 in equation 1

x + 3.5 = 8

x = 8 - 3.5 = $4.5

Put x = 4.5 and y = 3.5 in equation 3.

4.5 + 3.5 + z = 13.5

8 + z = 13.5

z = 13.5 - 8 = $5.5

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

d is the answer

step-by-step explanation: