Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution or an infinite number of solutions. X+y=9 4x+y=15 selecting an option will enable input for any required text boxes. If the selected option does not have any associated text boxes then no further input is required
To solve the system of linear equations by substitution, we can solve one equation for one variable and substitute it into the other equation.
From the first equation, we can solve for y:
x + y = 9
⇒ y = 9 - x
Now substitute this value of y into the second equation:
4x + y = 15
⇒ 4x + (9 - x) = 15
⇒ 4x - x = 15 - 9
⇒ 3x = 6
⇒ x = 2
Substitute this value of x back into the first equation to find y:
x + y = 9
⇒ 2 + y = 9
⇒ y = 9 - 2
⇒ y = 7
Therefore, the solution to the system of equations is x = 2 and y = 7. The system has one unique solution.