Plz help me how would you solve 4x + 2y = 18, 3x - 5y =20 by elemination

x = 5, y = -1

Step-by-step explanation:

Equation 1: 4x + 2y = 18

Equation 2: 3x - 5y = 20

In order to eliminate one of the variables , find the LCM of either x or y.

I chose to eliminate y.  The LCM of 2 & 5 is 10.

Multiply the entire equation so the coefficient of the variable equals the LCM.

Then add the equations and solve for the remaining variable.

5(4x + 2y = 18)       -->        20x + 10y = 90

2(3x - 5y = 20)      -->           6x  - 10y = 40

                                           26x          = 130  

                                          ÷26            ÷26

                                                x         =  5

Next, input x = 5 into either of the equations to solve for y.

Equation 1: 4x + 2y = 18

                 4(5) + 2y = 18

                  20  + 2y = 18

                -20            -20

                           2y = -2

                          ÷2     ÷2

                             y = -1

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.