The given system of equations have infinitely many solutions.
What is solution of a system of equations?
A solution of a system of equations is a list of numbers i.e. the value of variables that make all the of the equations true simultaneously.
What is slope intercept form of a line?
The slope intercept form of the line is y = mx + b, where m is the slope and b is y intercept.
When the two lines coincide to each other?
If there is no intercept difference between them ( intercept of two lines or system of equations) , then the line coincide to each other.
What is system of linear equations?
A system of linear equations is a set of equations which are satisfied by the same set of variables.
What is the solution to the system of linear equation?
The solution to a system of linear equation is the point at which the lines representing the linear equation intersect.
- A system of linear equations has no solution when the lines are parallel to each other.
- A system of linear equations has infinitely many solution, when the lines coincide to each other.
- A system of linear equations has one solutions when the line intersect at a point.
According to the given question
We have , a system of equations
[tex]x + y = 1[/tex]
⇒[tex]y = -x+1..(i)[/tex]
and
[tex]3y = -3x + 3[/tex]
⇒[tex]y = -x + 1..(ii)[/tex]
From equation (i) and (ii) we can see that there is no any intercept difference for the given system of equation. They have same slope and same intercept.
Therefore, the given system of linear equations coincide to each other, so they have infinitely many solutions.
Learn more about the system of linear equations here:
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