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. -4x+y=1 4x+4y=-16. 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 will isolate one variable in the first equation and substitute it into the second equation.
From the first equation, we can isolate y by adding 4x to both sides:
-4x + y = 1
y = 4x + 1
Now, we can substitute this expression for y in the second equation:
4x + 4(4x + 1) = -16
Simplifying the equation:
4x + 16x + 4 = -16
20x + 4 = -16
20x = -20
x = -1
Now that we have the value of x, we can substitute it back into the first equation to find y:
-4(-1) + y = 1
4 + y = 1
y = 1 - 4
y = -3
So the solution to the system of linear equations is x = -1 and y = -3.
Therefore, the system has one unique solution.