Solve the system of equations using the of substitution 8x+4y=15, x+y=3

Hi there!

8x + 4y = 15

x + y = 3

Use the second equation to solve for a particular variable since it is easier to isolate. We can begin by solving for y:

x + y = 3

Subtract y from both sides:

x = -y + 3

Substitute in this expression for x into the other equation:

8(-y + 3) + 4y = 15

Distribute and simplify:

-8y + 24 + 4y = 15

-4y + 24 = 15

-4y = -9

y = 9/4

Substitute in this value of y to solve for x:

8x + 4(9/4) = 15

8x + 9 = 15

8x = 6

x = 6/8 = 3/4

The values respectively are:

x = 3/4, y = 9/4

6.95 feet

Step-by-step explanation:

The shape of the cot is rectangular. A diagonal of the rectangle divides the rectangle into two Congruent Right Angled triangles. The length and width of the rectangle become the legs of the right triangle and the diagonal is the hypotenuse of the right triangle.

In order to find the length of the hypotenuse which is the diagonal in this case we can use the Pythagoras Theorem. According to the theorem, square of hypotenuse is equal to the sum of square of its legs. So for the given case, the formula will be:

Thus, rounded of to nearest hundredth foot, the diagonal distance from corner to corner is 6.95 feet