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There are several ways to do it - depending, in part, on the kind of equations. Sophisticated methods exist specifically for linear equations, among others.

However, for a start, you can combine equations (1) and (2), eliminating one variable; the same for equations (2) and (3), and for equations (3) and (4) (eliminating the same variable in every case). That leaves you with 3 equations with 3 variables.

Similarly, reduce the 3 equations in 3 variables, to 2 equations in 2 variables (eliminating the same variable in every case). Combine those into a single equation with 1 variable.

Example for eliminating a variable:

(Eq. 1) 5a + 3b - 3c + 8d = 28

(Eq. 2) 8a - 3b + 8c - 6d = 8

If you just add up the equations, you eliminate variable b. If you want to eliminate variable a, multiply the first equation by 8, and the second by (-5), then add the resulting equations.

Q: How do you solve the system of equations when you have 4 equations with 4 unknowns?

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There is not enough information to solve this. You have 2 equations and 4 unknowns. Here are the equations: Area = 2LW + 2LH + 2HW = 300 ; Volume = L*W*H The unknowns are Length, Width, Height, and Volume.

Solving equations in two unknowns requires two independent equations. Since you have only one equation there is no solution.

I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.

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To solve a system of equations, you need equations (number phrases with equal signs).

There is not enough information to solve this. You have 2 equations and 4 unknowns. Here are the equations: Area = 2LW + 2LH + 2HW = 300 ; Volume = L*W*H The unknowns are Length, Width, Height, and Volume.

Solving equations in two unknowns requires two independent equations. Since you have only one equation there is no solution.

Create a matrix of the coefficients of each equation. The solutions to the equations should make up the rightmost column of the matrix. Then, row reduce the matrix until you are able to rewrite the equations and solve them. The matrix should be a 4x5 matrix (4 rows and 5 columns) for four equations with four variables. This is known as a system of equations.

I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.

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y = 4x + 6As there are two unknowns, you need to have two equations to solve this out.Else you can simple write the values of x and y as:4x = y - 6x = (y - 6) / 4

Step 1: Determine your known variablesStep 2: Determine your unknown variablesStep 3: Determine the relationship (equations, etc.) between the two sets of variablesStep 4: Solve for any and all unknowns using any techniques you know

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y=3x-4 y=-2x+1