Solve the system of Linear Equations USING substitution method
x = y +4
2x + 2y = 16

x = 8

y = 4

Step-by-step explanation:

x = y + 4

2x + 2y = 16

Solve the system of equations

Substitution Method

We know that we need to use the substitution method, since we see that the first equation has x alone, we can substitute it with the x's in the second equation.

x = y + 4

2x + 2y = 16

2(y + 4) + 2y = 16

Distribute :

2y + 8 + 2y = 16

Add like terms :

4y + 8 = 16

Subtract 8 from both sides :

4y = 8

Divide 4 from both sides :

y = 4

Now that y is 4, substitute it into the first equation to get x :

x = (4) + 4

4 + 4

8

x = 8

answer: i think it is (1,-2)

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.