Solve using a system of two equations in two unknowns.
the length of a rectangle is 9 inches more than twice its
width. if the perimeter of the rectangle is 48 inches, find
its length and width.

Hello!

To solve this, first write two equations. We are given two facts about the situation, so we can write the equations accordingly.

Say the length of the rectangle is l, and the width is w.

The length of a rectangle is 9 inches more than twice its width: 2w + 9 = l, as you're adding 9 to two times the width.

The perimeter of the rectangle is 48 inches: The equation for perimeter is 2l + 2w, so we can just use that in this case to make the equation - 2l + 2w = 48

Now, set up the system of equations.

Now, we can already use substitution to solve. We get from one of the equations that l = 2w + 9, so we can substitute 2w + 9 for l in the other equation, and then solve for w.

2l + 2w = 48

2 (2w + 9) + 2w = 48

4w + 18 + 2w = 48

6w = 30

w = 5

We know one of our variables now. Now, all that's left to do is substitute 5 for w in one of the original equations to solve for l.

2w + 9 = l

2 (5) + 9 = l

10 + 9 = l

19 = l

Therefore, we now have our dimensions. The length of the rectangle is 19 inches, and the width is 5.

Hope this helps!

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!