Solve the system of equations - 8x - 5y = -13 and - 4x – 5y = 11 by
combining the equations.

(6,-7)

Step-by-step explanation:

subtract them:

-8x - 5y = -13

-4x - 5y = 11

you get

-4x = -24

so x = 6

plug x into the second equation:

-24 - 5y = 11

-5y = 35

y = -7

so your solution is (6,-7).

Your solution is (6, -7).

Step-by-step explanation:

Combining the equations is also known as substitution. This is done when you substitute one variable into another equation.

-8x - 5y = -13

-4x - 5y = 11

Let's change the second equation into one with one variable on each side.

-5y = 4x + 11

y = -4/5x - 11/5

Now, plug this into your first equation.

-8x - 5(-4/5x - 11/5) = -13

Distribute the -5 sign.

-8x + 4x + 11 = -13

Combine the like terms.

-4x + 11 = -13

-4x = -24

Isolate x by dividing both sides by -4.

x = -24/-4

x = 6

Now plug this back into either equation.

y = -4/5(6) - 11/5

Multiply.

y = -24/5 - 11/5

Subtract.

y = -35/5

Simplify.

y = -7

Your solution is (6, -7).

Check this by plugging in these values into the equation you have not checked yet.

-8(6) - 5(-7) = -13

-48 + 35 = -13

-13 = -13

Your solution is correct.

Hope this helps!

 B) 320 square centimeters

Explanation:

The base faces are the two triangles that are parallel to one another. We'll be ignoring those faces when computing the lateral surface area.

Instead, we focus on the three rectangles that form the sides. We can think standing the prism on one of the triangular faces, so that one triangle is the floor and the other triangle is the ceiling. The rectangular pieces are the walls of this room.

The bottom rectangle is 8 cm by 16 cm, so it has area 8*16 = 128 sq cm.The rectangle on the right is 6 cm by 16 cm, so it has area of 6*16 = 96 sq cm.The rectangle on the left is 6 cm by 16 cm, so it has area 6*16 = 96 sq cm.

The three areas then combine to 128+96+96 = 320 square cm which is the lateral surface area.

As a different approach, we can use this formula

LSA = p*h

where LSA is the lateral surface area, p is the perimeter of the base polygon, h is the height of the prism.

The base triangle has sides of 8, 6 and 6. So the perimeter is p = 8+6+6 = 20 cm. The height is h = 16 cm. The LSA is therefore,

LSA = p*h = 20*16 = 320 square cm.