# Write any four solutions for the following equation: 3x + y = 7

Last updated date: 22nd Mar 2023

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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.

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