Question

How do you solve the equation \[x - 2y = - 7\]?

Answer 1

Hint: We can use the slope-intercept method to solve this question. The slope-intercept method is a form in which we can calculate slope and intercept with the help of its form. The form is \[y = mx + c\] where ‘m’ is the slope and ‘c’ is the intercept.

Complete step by step solution:
The given equation is:
\[x - 2y = - 7\]
First, we will start by solving for \[y\]. We will try to make \[y\] alone. So, we will subtract \[x\] from both the sides, and then we will get:
\[ \Rightarrow x - 2y - x = - 7 - x\]
\[ \Rightarrow - 2y = - 7 - x\]
Now, we will divide all the terms from the equation by \[ - 2\], and we will get:
\[ \Rightarrow \dfrac{{ - 2y}}{{ - 2}} = \dfrac{{ - 7 - x}}{{ - 2}}\]
When we will simplify, then we will get:
\[ \Rightarrow \dfrac{{ - 2y}}{{ - 2}} = \dfrac{{ - 7}}{{ - 2}} + \dfrac{{ - x}}{{ - 2}}\]
Here, we will cancel out the common terms, and we will get:
\[ \Rightarrow y = \dfrac{{ - 7}}{{ - 2}} + \dfrac{{ - x}}{{ - 2}}\]
Now, we will again simplify the equation. We will shift the negative sign and we will get:
\[ \Rightarrow y = \dfrac{7}{2} + \dfrac{x}{2}\]
If we rewrite the equation, we will get:
\[ \Rightarrow y = \dfrac{x}{2} + \dfrac{7}{2}\]
Now, we will try to write the equation in the slope intercept form. The form has a general equation as:
\[y = mx + c\] where \[m = slope\,;\,c = y - \operatorname{int} ercept\]
According to this form, we will write our given equation as:
\[ \Rightarrow y = \dfrac{1}{2}x + \dfrac{7}{2}\]
Here, \[m = \dfrac{1}{2};\,c = \dfrac{7}{2}\]. Therefore, our slope is \[\dfrac{1}{2}\] and the y-intercept is \[\dfrac{7}{2}\].
We can choose any value of \[x\], and we will put that value in the equation to find the value of \[y\].
We will take \[1\] and replace it with \[x\]:
\[ \Rightarrow f(1) = \dfrac{1}{2} + \dfrac{7}{2}\]
When we simplify the equation, we will get:
\[ \Rightarrow f(1) = \dfrac{{1 + 7}}{2}\]
\[ \Rightarrow f(1) = \dfrac{8}{2}\]
\[ \Rightarrow f(1) = 4\]
So, we get that the value of \[y\]at \[x = 1\]is \[4\].
Next, we will take \[3\]and replace it with \[x\]:
\[ \Rightarrow f(3) = \dfrac{1}{2} \times 3 + \dfrac{7}{2}\]
\[ \Rightarrow f(3) = \dfrac{3}{2} + \dfrac{7}{2}\]
\[ \Rightarrow f(3) = \dfrac{{3 + 7}}{2}\]
\[ \Rightarrow f(3) = \dfrac{{10}}{2}\]
\[ \Rightarrow f(3) = 5\]
So, we get that the value of \[y\]at \[x = 3\] is \[5\].
When we create a table for the values of \[x\]and \[y\], we get:

X	Y
1	4
3	5

These are the solutions of the equation.

Note: This is a very easy method for solving. But there is another method through which we can solve. We have to represent \[x\]in terms of \[y\], or we can represent \[y\]in terms of \[x\]. This method is generally not suitable. We should prefer the slope-intercept method only.