# How do you solve #4x – y = 5# and #x + y = 10# and which method do you use?

##### 3 Answers

#### Explanation:

Here is the answer...

First take the second equation...

Now substitute

Substituting this value of

Therefore,

#### Explanation:

solve by elimination

substitute into

check in

See explanation.

#### Explanation:

The system is:

#{(4x-y=5),(x+y=10):}#

It can be solved using any of 3 methods:

**Using substitution:**

From the second equation we can calculate that:

If we put this in the first equation we get:

#4x-(10-x)=5#

#4x-10+x=5#

#5x-10=5#

#5x=15=>x=3#

Now we can calculate that

So the solution is

**By adding both equations:**

In the initial system the coefficients of

Now we can calculate the remaining variable

**Graphically**

Both equations represent linear functions, so we can solve the system by graphing the lines and seeing if they intersect:

graph{(y-4x+5)(x+y-10)((x-3)^2+(y-7)^2-0.05)=0 [-10, 10, -8, 8]}

As we can see the lines intersect at

The choice of method depends on the system of equations. Here the easiest (for me) is the second method but others may prefer different ones.