Question

Solve the system of equations. y=3x+2 y=x^2-4+2

Answer 1

The solutions to the system of equations are (4, 15) and (-1,-1)

How to solve the system of equations?

The system of equations is given as:

y=3x+2

y=x^2-4+2

Substitute y=3x+2 in y=x^2-4+2

3x + 2=x^2-4+2

Simplify

x^2 - 3x - 4 = 0

Expand

x^2 + x - 4x - 4x = 0

Factorize

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

This gives

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

Solve for x

x = 4 and x = -1

Substitute these values in y=3x+2

y = 3(4)+2 = 15

y = 3(-1)+2 = -1

Hence, the solutions to the system of equations are (4, 15) and (-1,-1)

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