1 First, we express Y through X in the first equation. Then we take Y out of the brackets in the second equation.
2 We write the Y-equivalent from the first equation in the second equation. So, we have the following:
3 We multiply (4 - X) by (1 + X) and write the new expression in the left-hand side of the equation. The right-hand side is still the same.
4 After that, we transfer everything to the left-hand side to make the expression equal to zero.
5 Then we change the signs to make the quadratic equation look more conventional.
6 To solve the quadratic equation we apply the quadratic formula which is true for any quadratic equation.
We see that in our equation
b is equal to -3
a is equal to 1
and c is equal to 2
So, we use these numbers instead of the letters and get the following:
7 Then we simplify the right-hand side.
8 The sign ± demonstrates that X can take two different values. We need to solve the expression for X1 and X2
9 Now we know the value of X1 and X2, and we need to find out Y1 and Y2. Let’s express them through X1 and X2 (see step 2).
(Y1 is equal to four minus two and is equal to two)
(Y2 is equal to four minus one and is equal to three)
10 Now we can see that the system of equations has two solutions. We write down both of them as necessary.
Solution: (2; 2) (1; 3)