Determine if the ordered pair ( -5,2) is a solution to the following system of equations.
x + 3y = 1
y = 3x + 17
x+3(3x+17)=? 1
-5+3(-15+17)=
-5+3(2)=
1=1
To determine if the ordered pair (-5,2) is a solution to the system of equations, substitute the values of x and y into both equations and see if the equations are true.
1. Substituting x = -5 and y = 2 into the first equation:
(-5) + 3(2) = 1
-5 + 6 = 1
1 = 1
The equation is true for the ordered pair (-5,2) in the first equation.
2. Substituting x = -5 and y = 2 into the second equation:
y = 3x + 17
2 = 3(-5) + 17
2 = -15 + 17
2 = 2
The equation is also true for the ordered pair (-5,2) in the second equation.
Since the ordered pair (-5,2) satisfies both equations, it is a solution to the system of equations.
To determine if the ordered pair (-5, 2) is a solution to the system of equations, we need to substitute the values of x and y into each equation and check if both equations are true.
1. Let's start with the first equation: x + 3y = 1.
Substituting x = -5 and y = 2, we get:
(-5) + 3(2) = 1
-5 + 6 = 1
1 = 1
The equation is true when x = -5 and y = 2.
2. Now let's check the second equation: y = 3x + 17.
Substituting x = -5 and y = 2, we get:
2 = 3(-5) + 17
2 = -15 + 17
2 = 2
The equation is also true when x = -5 and y = 2.
Since both equations are true, we can conclude that the ordered pair (-5, 2) is indeed a solution to the given system of equations.