Answer:
Please check the explanation.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x-3y=2\\ 2x+y=11\end{bmatrix}[/tex]
Multiplying the second equation i.e. 2x+y = 11 by 3 and then adding the result to the first equation would eliminate the variable y and the value of x can be determined.
3(2x+y) = 3(11)
6x+3y = 33
Now, adding 6x+3y = 33 to the first equation i.e. x-3y = 2
x - 3y = 2
+
6x + 3y = 33
__________
7x = 35
divide both sides by 7
7x/7 = 35/7
x = 5
so, the value of x = 5.
Therefore, we conclude that in order to solve the system of equations using elimination methods, we can multiply the second equation i.e. 2x+y = 11 by 3, and then adding the result to the first equation would eliminate the variable y and the value of x can be determined.
Hence, option (a) is true.
BONUS: SOLVING THE REMAINING PORTION to determine y
As
x = 5
substituing x = 5 in x - 3y = 2
x - 3y = 2
5 - 3y = 2
5 - 2 = 3y
3 = 3y
y = 1
Therefore,
x = 5
y = 1
