How many solutions will this system of equations have? y = −3.5x − 3.5 y = −3.5x + 3.5?
Linear equations are equations that have a degree equal to one. They have many applications in various fields.
Answer: The system of equations y = −3.5x − 3.5 and y = −3.5x + 3.5 will have no solutions.
Let's proceed step by step and see how we got the solution.
Explanation:
To check for the number of solutions in a system of linear equations as given, we need to check the equality of the ratios of their corresponding coefficients of the given variables.
Here, after rearranging, we have the given set of equations:
⇒ y + 3.5x + 3.5 = 0
⇒ y + 3.5x − 3.5 = 0
Here, the ratio of coefficients of variable y = 1 / 1 = 1
The ratio of coefficients of variable x = 3/5 / 3.5 = 1
The ratio of the constants = 3.5 / (-3/5) = -1
From the above calculations, we see that:
The ratio of coefficients of variable y = The ratio of coefficients of variable x ≠ The ratio of the constants.
Geometrically, this means that both the equations have the same slope, and hence are parallel, and cannot have an intersection point.
When the above condition is true, we have no solutions for a given system of equations.