Solve the problem:

A shopper purchased 5 T-Shirts and 3 pairs pants for $105. The next day, he purchased 4 T-shirts and 2 pair of
pants for $80. How much does each T-shirt and each pair of pants cost?

$15 And $10

Step-by-step explanation:

Let T-shirt’s be x and pants be y.

Firstly 5 T-shirts plus 3 pairs of pants cost $105

That’s

5x + 3y = 105

The next day 4 T-shirts and 2 pairs of pants cost $80.

That’s

4x + 2y = 80

Thus we have

5x + 3y = 105

4x + 2y = 80

Multiply equation one by 4 and equation two by 5

We have

20x + 12y = 420

20x + 10y = 400

Subtract equation 2 from 1

We’re left with

2y = 20

Divide both sides by 2

y = 20/2

y = 10

Now substitute 10 for y into any of the equations to get x.

Using equation one

We have

5x + 3 x 10 = 105

5x + 30 = 105

Subtract 30 from both sides

5x + 30 - 30 = 105 - 30

5x = 75

Divide both sides by 5

x = 75/5

= 15

Therefore each T-shirt cost $15 and each pant costs $10

it would be 6xy and -16xy.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!