Question

Solve the system of equations using the linear combination method. {4j−2k=265j−2k=35 Enter your answers in the boxes.

Answer 1

Solution :- The given system of equations are

`4j-2k=26\\\text{and}\ 5j-2k=35`

Now by linear combination method , write them in columns

`4j-2k=26\  [.......(1)]\\\\5j-2k=35\ [........(2)]\\\text{Now subtract (1) from (2) ,we get}\\5j-2k=35\\-4j+2k=-26\\\Rightarrow\ j=9\\\text{substituting the value of j in (1),we get}\\4(9)-2k=26\\\Rightarrow\ 36-2k=26\\\Rightarrow\ 2k=36-26=10\\\Rightarrow\ k=5`

so the answer is j=9 and k=5.

Answer 2

You can break down linear combination method in following steps:
1) Arrange the like terms in columns (x bellow x, y bellow y...)
2) Multiply one or both equations until you "kill" one of the terms
This means that coefficients on one of your terms have the same value but have opposite signs.
3) Add equations and repeat steps 1 and 2 if you had more than two equations to start with.

So to start with we write equations with like terms in columns.

4j−2k=26
5j−2k=35
All we have to do now is multiply the second equation by (-1).

4j -2k=26
-5j+2k=-35
Now we can add them together and solve for j.

-j=-9
j=9

We can find k simply by plugging in j=9.

4(9)−2k=26
36−2k=26
2k=36-26
k=5