You can use elimination method when solving a system of equations and you can quickly eliminate one variable by adding or subtracting your equations together.
Practice Questions
Solve using Elimination
\(\textbf{1)}\) \(3x+y=10\)
\(\hspace{11pt}x-y=2\)
\(\textbf{2)}\) \(x-4y=12\)
\(\hspace{11pt}x+3y=-2\)
\(\textbf{3)}\) \(2x+3y=11\)
\(\hspace{11pt}x+y=3\)
\(\textbf{4)}\) \(x-y=-6\)
\(\hspace{11pt}5x+2y=12\)
\(\textbf{5)}\) \(7x+4y=31\)
\(\hspace{11pt}3x+2y=15\)
\(\textbf{6)}\) \(5x-4y=9\)
\(\hspace{11pt}7x+3y=4\)
\(\textbf{7)}\) \(15x-3y=126\)
\(\hspace{11pt}2x+5y=33\)
\(\textbf{8)}\) \(2x-y=-1\)
\(\hspace{11pt}3x+4y=-7\)
\(\textbf{9)}\) \(2x-7y=-18\)
\(\hspace{11pt}3x+8y=47\)
\(\textbf{10)}\) \(3x+2y=12\)
\(\hspace{15pt}5x-4y=-2\)
\(\textbf{11)}\) \(x+2y=12\)
\(\hspace{15pt}2x+4y=10\)
\(\textbf{12)}\) \(4x-2y=12\)
\(\hspace{15pt}-2x+y=-6\)
\(\textbf{13)}\) \(4x+2y=22\)
\(\hspace{15pt}3x-2y=6\)
Challenge Questions
Solve using Elimination
\(\textbf{14)}\) \(y=-2x+5\)
\(\hspace{15pt}y=x-1\)
\(\textbf{15)}\) \(y=3x+2\)
\(\hspace{15pt}2y-6x=-6\)
\(\textbf{16)}\) \(y=-3x+5\)
\(\hspace{15pt}9x+3y=15\)
\(\textbf{17)}\) \(4x+3y=12\)
\(\hspace{15pt}y=4\)
\(\textbf{18)}\) \(2x-3y=0\)
\(\hspace{15pt}y=x-1\)
See Related Pages\(\)
\(\bullet\text{ System of Equations Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Wolframalpha.com)}\)
\(\bullet\text{ Solving Systems with Substitution}\)
\(\,\,\,\,\,\,\,\,y=−2x+5\)
\(\,\,\,\,\,\,\,\,y=x-1…\)
\(\bullet\text{ Graphing Systems of Inequalities}\)
\(\,\,\,\,\,\,\,\,y\lt-3x+2 \)
\(\,\,\,\,\,\,\,\,y\ge\frac{1}{2}x-1…\)
\(\bullet\text{ 3 variable systems}\)
\(\,\,\,\,\,\,\,\,2x+3y−5z=−7 \)
\(\,\,\,\,\,\,\,\,3x−6y+4z=3 \)
\(\,\,\,\,\,\,\,\,x+4y+2z=15…\)
\(\bullet\text{ Nonlinear Systems}\)
\(\,\,\,\,\,\,\,\,x^2+y^2=8 \)
\(\,\,\,\,\,\,\,\,y=x…\)
In Summary
Solving systems of equations with elimination involves using the values from one equation to eliminate a variable in the other equation. This is a very common method for solving systems of equations with two or more variables.
Solving systems of equations with elimination is typically covered in a high school or college algebra class.
One real-world example of solving systems of equations with elimination is in finding the dimensions of a rectangular box given the volume and the surface area. Another example is in finding the cost of a product given the total cost and the number of units.
The 3 most common methods for solving systems of linear equations is substitution, elimination and graphing.
In a system of equations, a solution is considered dependent if there is more than one solution to the system. This means that the equations are not independent of each other, and one equation can be derived from the other. In this case, the system is said to be dependent because the solutions to the equations are not unique.
An inconsistent system of equations is one that has no solutions. This means that the equations in the system contradict each other and cannot be satisfied simultaneously.