for each ordered pair, determine whether it a solution to the systems of equations
y=7x-4
-14x+2y=-8
(x,y) is it a solution? yes/no
(-2,5)
(3,17)
(0,4)
(-1,-11)
To determine whether each ordered pair is a solution to the system of equations, we substitute the x and y values into both equations to see if they are satisfied.
1) For the ordered pair (-2,5):
Substituting the values into the equations:
y = 7x - 4 -> 5 = 7(-2) - 4 -> 5 = -14 - 4 -> 5 = -18 (The equation is not satisfied)
-14x + 2y = -8 -> -14(-2) + 2(5) = -8 -> 28 + 10 = -8 -> 38 = -8 (The equation is not satisfied)
The ordered pair (-2,5) is not a solution to the system of equations.
2) For the ordered pair (3,17):
Substituting the values into the equations:
y = 7x - 4 -> 17 = 7(3) - 4 -> 17 = 21 - 4 -> 17 = 17 (The equation is satisfied)
-14x + 2y = -8 -> -14(3) + 2(17) = -8 -> -42 + 34 = -8 -> -8 = -8 (The equation is satisfied)
The ordered pair (3,17) is a solution to the system of equations.
3) For the ordered pair (0,4):
Substituting the values into the equations:
y = 7x - 4 -> 4 = 7(0) - 4 -> 4 = -4 (The equation is not satisfied)
-14x + 2y = -8 -> -14(0) + 2(4) = -8 -> 0 + 8 = -8 -> 8 = -8 (The equation is not satisfied)
The ordered pair (0,4) is not a solution to the system of equations.
4) For the ordered pair (-1,-11):
Substituting the values into the equations:
y = 7x - 4 -> -11 = 7(-1) - 4 -> -11 = -7 - 4 -> -11 = -11 (The equation is satisfied)
-14x + 2y = -8 -> -14(-1) + 2(-11) = -8 -> 14 - 22 = -8 -> -8 = -8 (The equation is satisfied)
The ordered pair (-1,-11) is a solution to the system of equations.
In summary:
(-2,5) is not a solution
(3,17) is a solution
(0,4) is not a solution
(-1,-11) is a solution