Question

What is the solution to this system of equations using the linear combination method? {3x y=42x y=7

Answer 1

The solution to the system of equations using the linear combination method is (C) (−3, 13).

What is the linear combination method?

• Linear combination is the process of combining two algebraic equations in such a way that one of the variables is removed.
• A linear combination can be performed using addition or subtraction.

To find the solution to the system of equations using the linear combination method:

Solve,

$\left\{\begin{array}{l}3 x+y=4 \\2 x+y=5\end{array}\right.$

Using the linear combination method:

• We prefer to work with integers in general, so if we wanted to cancel x-terms, we would most likely multiply the second equation by 3 and the first equation by -2, then add the results of those operations.

This would result in:

• 3 (2x + y) -2(3x +y) = 3(7) -2(4)
• y = 13

Since only one option (C) has the value y = 13 and we know that the correct value of y is 13, then the correct option is (A) (-1, 7) and y = 7.

Therefore, the solution to the system of equations using the linear combination method is (C) (−3, 13).

Know more about the linear combination method here:

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The correct question is given below:
What is the solution to the system of equations using the linear combination method? {3x+y=42x+y=5

(A) (−1, 7)

(B) (−3, 12)

(C) (−3, 13)

(D) (0, 4)