First, the substitution method

Method of substitution is a common method to solve equations. When we encounter a complex equation, we can first express one of its variables with another, and then substitute it into the equation to get a simplified equation, and then solve it.

For example, we consider solving equations 2x+3y=7 and x+y=4. We can use Y in the first equation to represent X in the second equation and get X = 4-Y, and then substitute X into the first equation and get 2(4-y)+3y=7. After simplification, you can get 5y= 1, and then you can get y= 1/5. Substituting y into x=4-y, you can get x=4- 1/5= 19/5.

So the solution of the original equation is x= 19/5 and y= 1/5.

Second, the elimination method

Elimination method is a common method to solve equations. It eliminates some variables by adding or subtracting some equations in the equation set, obtains a simplified equation set, and then solves it.

For example, we consider solving equations 2x+3y = 7 and x+y = 4. We can multiply x in the second equation by 2 to get 2x+2y=8, and then subtract this equation from the first equation to get y= 1. Substituting y into the second equation, we can get x+ 1=4 and x=3. Therefore, the solution of the original equations is x=3, y= 1.

Thirdly, factorization method.

Factorization is a method to solve a quadratic equation with one variable. The general form of unary quadratic equation is ax 2+bx+c = 0, where a, b and c are constants and a≠0.

For example, we consider solving the equation x 2-5x+6 = 0. First, we can factorize the equation into (x-2)( x-3)=0. According to the nature of factorization, the equation holds only when (x-2)=0 or (x -3)=0. The solution is x=2 or x=3. So the solution of the original equation is x = 2 and x = 3.