Write any four solutions for the following equation: 3x + y = 7
Last updated date: 22nd Mar 2023
•
Total views: 309.3k
•
Views today: 2.87k
Answer
309.3k+ views
Hint- Here, we will be finding out the points which satisfy the given equation because those are the solutions to the given equation.
Given equation is $3x + y = 7 \Rightarrow y = - 3x + 7{\text{ }} \to {\text{(1)}}$
Solutions for any equation are determined by finding out the points which will be satisfying the given equation.
Put $x = 0$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 0 + 7 \Rightarrow y = 7$
So, the first solution is $\left[ {0,7} \right]$
Put $x = 1$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 1 + 7 = - 3 + 7 \Rightarrow y = 4$
So, the second solution is $\left[ {1,4} \right]$
Put $x = 2$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 2 + 7 = - 6 + 7 \Rightarrow y = 1$
So, the third solution is $\left[ {2,1} \right]$
Put $x = 3$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 3 + 7 = - 9 + 7 \Rightarrow y = - 2$
So, the fourth solution is $\left[ {3, - 2} \right]$
Therefore, any four solutions to the given equation are $\left[ {0,7} \right]$, $\left[ {1,4} \right]$, $\left[ {2,1} \right]$ and $\left[ {3, - 2} \right]$.
Note- As we know that the general equation of any straight line having m slope and y intercept as c is given by y = mx + c. Clearly, the given equation is an equation of a straight line with a slope of - 3 and y intercept as 7. In this problem, there can be multiple answers possible since there will be many points satisfying the given equation of straight line.
Given equation is $3x + y = 7 \Rightarrow y = - 3x + 7{\text{ }} \to {\text{(1)}}$
Solutions for any equation are determined by finding out the points which will be satisfying the given equation.
Put $x = 0$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 0 + 7 \Rightarrow y = 7$
So, the first solution is $\left[ {0,7} \right]$
Put $x = 1$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 1 + 7 = - 3 + 7 \Rightarrow y = 4$
So, the second solution is $\left[ {1,4} \right]$
Put $x = 2$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 2 + 7 = - 6 + 7 \Rightarrow y = 1$
So, the third solution is $\left[ {2,1} \right]$
Put $x = 3$, the value of y is evaluated from equation (1) as under
$ \Rightarrow y = \left( { - 3} \right) \times 3 + 7 = - 9 + 7 \Rightarrow y = - 2$
So, the fourth solution is $\left[ {3, - 2} \right]$
Therefore, any four solutions to the given equation are $\left[ {0,7} \right]$, $\left[ {1,4} \right]$, $\left[ {2,1} \right]$ and $\left[ {3, - 2} \right]$.
Note- As we know that the general equation of any straight line having m slope and y intercept as c is given by y = mx + c. Clearly, the given equation is an equation of a straight line with a slope of - 3 and y intercept as 7. In this problem, there can be multiple answers possible since there will be many points satisfying the given equation of straight line.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
