Question

X y=4, -9x -9y=-36 solve by substitution

Answer 1

To solve the system of equations using substitution, isolate one variable in one equation and substitute it into the other equation. The solution is (x,y) = (2,2) or (-2,-2).

Step-by-step explanation:

To solve the system of equations using substitution, we need to isolate one variable in one equation and substitute it into the other equation.

1. Start with the first equation: xy = 4. Solve for x: x = 4/y.
2. Substitute x = 4/y into the second equation: -9(4/y) - 9y = -36.
3. Simplify the equation: -36/y - 9y = -36.
4. Combine like terms and multiply through by y to clear the fraction: -36 - 9y^2 = -36y.
5. Rearrange the equation and set it to zero: 9y^2 - 36y - 36 = 0.
6. Factor the quadratic equation: (3y - 6)(3y + 6) = 0.
7. Solve for y: y = 2 or y = -2.
8. Substitute the values of y back into x = 4/y to get x: when y = 2, x = 4/2 = 2; when y = -2, x = 4/(-2) = -2.

The solution to the system of equations is (x,y) = (2,2) or (-2,-2).