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Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. Hint: use addition property of equality and multiplication property of equality in your answers 5x + 2y = 7 3x - y = 2 A. To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations B. Why is this multiplication allowed? C. What variable will be eliminated when the equations are combined after the multiplication? D. Next, add the equations together. Your answer should be a single equation with one variable. E. Why can you add the equations? F. Solve the equation for x. G. Substitute x back into one of the equations to solve for y. H. What is the solution to the system of equations?

Respuesta :

Answer:

Explained below.

Step-by-step explanation:

The system of two equations is:

[tex]5x+2y=7...(i)\\\\3x-y=2...(ii)[/tex]

Step A:

To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations.

[tex]5x+2y=7\\\\6x-2y=4[/tex]

Step B:

The multiplication is performed to simplify the elimination process.

Step C:

The variable that will be eliminated when the equations are combined after the multiplication is y.

Step D:

Next, add the equations together. Your answer should be a single equation with one variable.

[tex]5x+2y=7\\ +\\6x-2y=4\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\11x=11[/tex]

Step E:

We can add the equation because both the equation are in the same format, i.e. ax + by = c.

Step F:

Solve the equation for x.

11x = 11

x = 1

Step G:

Substitute x back into one of the equations to solve for y.

[tex]5x+2y=7\\\\(5\times 1)+2y=7\\\\5+2y=7\\\\2y=7-5\\\\2y=2\\\\y=1[/tex]

Step H:

The solution to the system of equations is: (x, y) = (1, 1).

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