A system of linear equations is essentially a collection of conditions that must be satisfied by specific variables, for both of the linear equations.
A system of linear equations is essentially a collection of conditions that must be satisfied by specific variables, for both of the linear equations.
If we have a system of linear equations with two variables, we need to find specific and that satisfy both equations together.
Example of a simple system of equations:
Solving a system of equations is essentially finding and that satisfy both the first equation and the second equation.
In this case, the solution to the system of equations is: ,
When we substitute these values, we get two equations that indeed hold true.
A system of linear equations with two variables has several methods of solution, and in this article we will focus on the algebraic method.
It all depends on the equations presented to us and what we are asked to do.
You might encounter a requirement to solve the system of equations graphically, and then you can easily do it using our guide - solving a system of equations with two unknowns graphically.
However, if you have the choice and you can choose whichever solution method you want, it's usually better to choose the algebraic way.
Drawing equations on a graph isn't always easy, and the graphical method sometimes takes longer than the algebraic method.
Therefore, we suggest that if not required, keep the ruler in your pencil case and avoid unnecessary drawings.
To solve a system of equations with two variables quickly - you'll need to know the algebraic method.
As its name implies, a method that uses algebra - meaning mathematical laws, solving exercises / equations without drawings.
Let's divide the algebraic solution methods into two approaches-
We will explain each one of them and provide tips for choosing the best method for your system.
Solve the above set of equations and choose the correct answer.
\( (I)-5x+4y=3 \)
\( (II)6x-8y=10 \)
Solve the above set of equations and choose the correct answer.
\( (I)-2x+3y=4 \)
\( (II)x-4y=8 \)
Solve the following equations:
\( (I)2x+y=9 \)
\( (II)x=5 \)
Solve the following equations:
\( (I)x+y=18 \)
\( (II)y=13 \)
Solve the following system of equations:
\( \begin{cases}
x-y=5 \\
2x-3y=8
\end{cases} \)
Solve the above set of equations and choose the correct answer.
Solve the above set of equations and choose the correct answer.
Solve the following equations:
Solve the following equations:
Solve the following system of equations:
Solve the following system of equations:
\( \begin{cases}
-8x+5y=3 \\
10x+y=16
\end{cases} \)
Solve the above set of equations and choose the correct answer.
\( (I)7x-4y=8 \)
\( (II)x+5y=12.8 \)
Solve the above set of equations and choose the correct answer.
\( (I)-8x+3y=7 \)
\( (II)24x+y=3 \)
Find the value of x and and band the substitution method.
\( \begin{cases} -x-2y=4 \\ 3x+y=8 \end{cases} \)
Find the value of x and and band the substitution method.
\( \begin{cases} x+y=5 \\ 2x-3y=-15 \end{cases} \)
Solve the following system of equations:
Solve the above set of equations and choose the correct answer.
Solve the above set of equations and choose the correct answer.
Find the value of x and and band the substitution method.
Find the value of x and and band the substitution method.
Solve the following system of equations:
\( \begin{cases}
2x-\frac{1}{5}y=18 \\
3x+y=6
\end{cases} \)
Solve the above set of equations and choose the correct answer.
\( (I)\frac{1}{3}x-4y=5 \)
\( (II)x+6y=9 \)
Find the value of x and and band the substitution method.
\( (I)-5x+9and=18 \)
\( (II)x+8and=16 \)
Find the value of x and and band the substitution method.
\( (I)-x+3and=12 \)
\( (II)4x+2and=10 \)
Solve the above set of equations and choose the correct answer.
\( (I)\frac{1}{2}x+\frac{7}{2}y=10 \)
\( (II)-3x+7y=12 \)
Solve the following system of equations:
Solve the above set of equations and choose the correct answer.
Find the value of x and and band the substitution method.
Find the value of x and and band the substitution method.
Solve the above set of equations and choose the correct answer.