Question

How do you solve the following system: $7x-5y=-11,7x-y=10$ ?

Answer 1

Hint: To solve this problem, we will try to do it using the substitution method. Starting with, we will get the value of x from the first equation. Putting the value of x in the second equation, we will get the equation including only y and numbers. Thus, we get the value of y. Using the value of y, we can find the value of x and our solution.

Complete step by step answer:
According to the problem, we are given two equations, $7x-5y=-11,7x-y=10$.
So, to find the value of x and y, we will try to do it with the substitution method.
Form the first equation, we have, $7x-5y=-11$
Now, we will try to find the value of x from this equation.
Putting 5y on the right side,
$\Rightarrow 7x=5y-11$
Dividing both sides by 7,
$\Rightarrow x=\dfrac{1}{7}\left( 5y-11 \right)$
Now, if we have the second equation, we get,
$7x-y=10$
We will try now to put the value of x we had from the first equation.
Thus, we get,
$\Rightarrow 7\times \dfrac{1}{7}\left( 5y-11 \right)-y=10$as, $x=\dfrac{1}{7}\left( 5y-11 \right)$
So, simplifying, we get,
$\Rightarrow \left( 5y-11 \right)-y=10$
Now, adding and subtracting, $4y-11=10$
So, $4y=21$
Then, we are getting the value of y as, $\dfrac{21}{4}$ .
Now, we will put the value of y in the first equation to get the value of x.
So, putting the value,
$\Rightarrow 7x-5\times \dfrac{21}{4}=-11$
Multiplying,
$\Rightarrow 7x-\dfrac{105}{4}=-11$
Changing the sides,
$\Rightarrow 7x=\dfrac{105}{4}-11$
Again, adding and subtracting,
$\Rightarrow 7x=\dfrac{105-44}{4}$
Getting,
$\Rightarrow 7x=\dfrac{61}{4}$
So, we have the value of x as, $x=\dfrac{61}{28}$, dividing both sides by 7.
Hence, the solution we get is, $x=\dfrac{61}{28}$and $y=\dfrac{21}{4}$.

Note:
If you have two different equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing. Addition or subtraction method is also known as the elimination method.