Question

Use substitution to solve the system y=-1/2x², y=x-4

Answer 1

Using substitution, the system of equations y=-1/2x² and y=x-4 are solved. Factoring the resultant quadratic equation, the solutions are determined to be x = -4 and x = 2, and by substituting these values back into the original equations, the corresponding y values are -8 and -2, respectively.

Step-by-step explanation:

To solve the system of equations using substitution, you take one equation and solve for one variable, and then substitute that expression into the other equation. In this case, we have two equations:

• y=-1/2x²
• y=x-4

Since both equations equal y, we can set them equal to each other to find the value of x.

(-1/2)x² = x - 4

Now, solve this quadratic equation for x:

1. Multiply everything by -2 to get rid of the fraction: x² + 2x - 8 = 0
2. Factor or use the quadratic formula to solve for x: (x+4)(x-2) = 0
3. Set each factor equal to zero: x+4 = 0 or x-2 = 0, which gives us x = -4 or x = 2.

Next, substitute the x values back into one of the original equations to solve for y:

• For x = -4: y = (-4) - 4 = -8
• For x = 2: y = 2 - 4 = -2

Thus, the solutions to the system of equations are (-4, -8) and (2, -2).