Question

A system of equations is given below. For what value(s) of x is f(x)=g(x) ?

f(x)=x2+3x

g(x)=x+3

Answer 1

`\large{f(x) = g(x)} \\ \large{ {x}^(2) + 3x = x + 3}`

Since we are solving the quadratic equation because the highest degree in the equation is second. We arrange in the form of ax²+bx+c = 0.

`\large{ {x}^(2) + 3x - x - 3 = 0}`

Combine like terms.

`\large{ {x}^(2) + 2x - 3 = 0}`

Solve the equation by factoring.

`\large{(x + 3)(x - 1) = 0} \\ \large{x = - 3,1}`

Hence the values of x that make f(x) = g(x) are -3 and 1.

Answer

• x = -3,1

Let me know if you have any doubts!