Question

Part A)

Please solve this system of equations using the elimination method ONLY.

3x - 2t = 4
2x - 5 = -t

Part B)
Which number is the most convenient to multiply by when solving this linear system of equations by elimination?

A) -3
B) -1
C) 1
D) 2

Thank you in advance.

Answer 1

D) 2

Explanation:

When solving a system of equations using elimination, it often works well to start with them in a form that has all of the variables on the same side of the equal sign. Putting the second equation into standard form will accomplish that:

• 3x -2t = 4
• 2x +t = 5

To eliminate one of the variables from the system, the equations are multiplied by numbers and combined (added or subtracted) so that the coefficient of one of the varibles becomes 0.

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Choosing a multiplier

The coefficients of x are 3 and 2. If we are to eliminate x, we either need to multiply one equation by a rational number (2/3 or 3/2), or we need to multiply the two equations by two different numbers (2, 3).

The coefficients of y are -2 and 1. If we are to eliminate y, it is convenient to multiply the second equation by 2. This is probably the most convenient choice.

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Solution

Multiplying the second equation by 2 and adding it to the first equation, we have ...

(3x -2t) +2(2x +t) = (4) +2(5)

7x = 14 . . . . . simplify; the y-variable is eliminated

x = 2 . . . . . . divide by 7

Using the original second equation, we have ...

2(2) -5 = -t = -1

t = 1

So, the solution is (x, t) = (2, 1).