$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$ [duplicate]

$K$ is field. $a_1$,$a_2$ elements of $K$. Show that $(x_1-a_1,x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$.

$K[x_1,x_2]$ is UFD so if $K[x_1,x_2]/(x_1-a_1,x_2-a_2)$ is field then $(x_1-a_1,x_2-a_2)$ is maximal ideal.

If I can show that $K[x_1,x_2]/(x_1-a_1,x_2-a_2)$ isomorphic to $K$, we can verify that $(x_1-a_1,x_2-a_2)$ maximal ideal of $K[x_1,x_2]$.

thanks for helps and comments.

Consider the following map (slightly modified the suggestion of @DonAntonio in comments): $$\phi:K[x,y]\to K,\quad \phi(f(x,y)):=f(a,b)$$ Then show that its kernel is just the ideal $(x-a,\,y-b)$ and its image contains $1$, so it is surjective, then use the first isomorphism theorem.