Solve the system of equations by substitution. (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as​ needed.)

Question

y = x^2 - 3x - 7
y = -2x^2 - 4x - 3

Answer 1

To solve the system of equations by substitution, we need to set the two expressions for y equal to each other.

So we have:

x^2 - 3x - 7 = -2x^2 - 4x - 3

Next, we can combine like terms by moving all the terms to one side of the equation:

3x^2 - x - 4 = 0

Now, we can solve this quadratic equation. However, to simplify the calculation, let's factorize the equation:

(3x + 4)(x - 1) = 0

Setting each factor equal to zero gives us two possible solutions:

3x + 4 = 0 or x - 1 = 0

Solving the first equation, we have:

3x = -4
x = -4/3

Solving the second equation, we have:

x = 1

So the possible solutions for the system of equations are x = -4/3 or x = 1.

Now, let's substitute these values of x back into one of the original equations (let's use the first one):

y = (1)^2 - 3(1) - 7
y = 1 - 3 - 7
y = -9

Therefore, the solutions to the system of equations are (-4/3, -9) and (1, -9).