Question

Solve the system. x+y=8 2x²-y=-5

Answer 1

To solve the system of equations x+y=8 and 2x²-y=-5, we can use the substitution or elimination method. Let's use the elimination method. Multiply the first equation by 2 to make the coefficients of x equal and add the second equation to the modified first equation. Rearrange the resulting equation into a quadratic equation and solve it to find the values of x. Substitute the value of x back into one of the original equations to find the value of y.

Step-by-step explanation:

To solve the system of equations x+y=8 and 2x²-y=-5, we can use the substitution or elimination method. Let's use the elimination method.

Multiply the first equation by 2 to make the coefficients of x equal:

• 2(x+y) = 2(8)
• 2x+2y = 16

Now, add the second equation to the modified first equation:

• (2x+2y) + (2x²-y) = 16 + (-5)
• 2x+2x²+y-y = 11
• 2x²+3x = 11

This is a quadratic equation. Rearrange it to get:

• 2x²+3x-11 = 0

Now, we can solve this quadratic equation to find the values of x. Once we have the value of x, we can substitute it back into either of the original equations to find the value of y.