# System of Equations

Solve the system of equations:

3x + y = -7

x - y = -5

Solve the system of equations:

3x + 2y = 18

y = 3x

Which of the following is true of a base period for an index number?

The numerator spears

It appears in the denominator

It must have occurred after the year 1980

It cannot be less than 100

https://brainmass.com/math/linear-algebra/system-of-equations-index-numbers-405331

#### Solution Preview

Solve the system of equations:

3x + y = -7

x - y = -5

METHOD: Solve the second equation for x, then plug that into the first equation. Simplify to solve for y, then solve for x.

Solve second equation for x:

x - y = -5

x = y - 5

Plug result into first equation:

3x + y = -7

3(y - 5) + y = -7

3y - 15 + y = -7

4y - 15 = -7

4y = 8

y = 2

Use ...

#### Solution Summary

This solution explains how to solve the given system of equations and how to solve a question involving the base period of an index number.

Differential Equations - Systems of Equations, Laplace Transform System of Equations.

I am looking for help with review problems for my final exam. I narrowed down the problems I am have the most difficulty with and need help with. I need the problems worked out so I can practice the appropriate steps for success on the final next week.

1. A 32 pound weight stretches a spring 2 Feet. The mass is then released from an initial position of 1 foot below the equilibrium position. The surrounding medium offers a damping force of 8 times the instantaneous velocity. Find the equation of motion if the mass is driven by an external force of 2cos5t.

2. Solve the system where X and Y are functions of t:

dx/dt = 4x - y

dy/dt = 2x + y

3. dx/dt + 3x + dy/dt = 1 x(0) = 0

dx/dt ? x + dy/dt - y = e^t y(0) = 0

4. Use Laplace Transforms to solve the system where X and Y are functions of t:

dx/dt ? 5x ? 4y = 0 x(0) = 1

5. Dy/dt + x ? y = 0 y(0) = -1

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