Solving Linear Systems by Multiplying First

Which of the following is a good start when using the elimination method to solve this system?

• multiplying the second equation by 1

• multiplying the first equation by -2

• multiplying the second equation by -1

• multiplying the first equation by 2

Answer explanation

The idea behind the elimination method is to cancel one of the variables. In order for this to be possible, the coefficients of this variable need to have the same absolute value and opposite signs.

In this example, if we multiply the second equation by −1, we would then be able to add the variable x in the first equation with −x in the second one which will result to cancellation of the said variable.

Therefore, the correct answer is multiplying the second equation by −1.

Solve the given system of linear equations.

Answer explanation

Which two equations would help you eliminate the variable y?

Answer explanation

To eliminate the variable y, both coefficients from the two equations should be additive inverses of each other.

The LCM of 4 and 9 is 36. Thus, you multiply the first equation by 9:

9(5x+4y=−30)

45x+36y=−270

Then, you multiply the second equation by 4:

4(3x−9y=−18)

12x−36y=−72

The new equations can now be added and the y variables can now be eliminated.

Solve the following system of linear equations:

Answer explanation

Solve the system by multiplication.
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Look at this system of equations:      4x -  y = -10   x + 3y =   -8 Which of the following statements describes the most logical first step in solving this system?

• Multiply the top equation by -4

• Multiply the bottom equation by -4

• Multiply the top equation by -1

• Multiply the bottom equation by -1

what would the top equation become when you multiply everything by -1?

• 2x - 6y = 20

• -2x - 6y = -20

• -2x + 6y = 20

• -2x + 6y = -20

Look at this system of equations:      4x -  y = -10   x + 3y =   -8Which of the following statements describes the most logical first step in solving this system?

• Multiply the top equation by -4

• Multiply the bottom equation by -4

• Multiply the top equation by -1

• Multiply the bottom equation by -1

Find the solution:
2x-5y=15
3x+y=31

• (10,1)

• (13, -8)

• (-10,-7)

• No Solution

What would the top equation become when you multiply everything by -1?

• 2x - 6y = 20

• -2x - 6y = -20

• -2x + 6y = 20

• -2x + 6y = -20