Question

A system of equations is shown below: 5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

Answer 1

Answer:

Student should show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.

Step-by-step explanation:

Given System of equations is 5x + 2y = 3 (equation 1) and 2x - 3y = 1 (equation 2)

Second System of equations is 2x - 3y = 1 and 7x - y = 4

How we got  7x - y = 4

Step 1: Multiply 2x - 3y = 1 by 1, we get the same 2x - 3y = 1

Step 2: Add 5x + 2y = 3 with 2x - 3y = 1

5x + 2x + 2y - 3y = 1

7x - 3y = 1

We have got second equation 7x - 3y = 1

Thus, Student should show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.

Answer 2

The new system of equations the student can use for the proof is:

7x - y = 4

2x - 3y = 1

What is the Solution to a System of Equations

The solution is simply the value of x and y that makes both equations true in the system.

Given:

5x + 2y = 3 --> eqn. 1

2x - 3y = 1 --> eqn. 2

Replacing equation 1 with the sum of eqn. 1 and a multiple of eqn. 2, we would have:

7x - y = 4

Therefore, the new system of equations the student can use for the proof is:

7x - y = 4

2x - 3y = 1

Learn more about the system of equations on:

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