
Find the solution for the system of equations and .
Answer
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Hint: The equation given in the question has two variables “x” and “y” that are linear equations in two variables. These are also called simultaneous equations also known as systems of equations that contain multiple variables. These equations can be solved by methods like substitution method, elimination method.
Complete step-by-step answer:
When one variable can be easily isolated in one of the two equations then this can be solved as a substitution method. The first equation should be solved for one variable. The solved equation should be substituted into the second equation.
Hence solving the first equation for “y” we have,
Now substituting for “y” in the second equation and solving for “x” we have,
Expanding the brackets by multiplying the negative sign we have,
Adding both the sides in left hand side and right hand side we have,
Dividing by ,
Cancelling and dividing by ,
Now substituting for “x” in the solution to the first equation and calculating for “y” we have,
So, the correct answer is “x = 4 and y = 2”.
Note: The solution should be tested by substituting into both the equations and making sure that the equations hold true. The solution should be substituted for the second variable back into the first equation and should be solved for the first variable. Mathematically a solution is simply a pair of points that make a series of equations true. Graphically represented, a solution is a series of points where the lines of the equations intersect.
Complete step-by-step answer:
When one variable can be easily isolated in one of the two equations then this can be solved as a substitution method. The first equation should be solved for one variable. The solved equation should be substituted into the second equation.
Hence solving the first equation for “y” we have,
Now substituting
Expanding the brackets by multiplying the negative sign we have,
Adding
Dividing by
Cancelling
Now substituting
So, the correct answer is “x = 4 and y = 2”.
Note: The solution should be tested by substituting into both the equations and making sure that the equations hold true. The solution should be substituted for the second variable back into the first equation and should be solved for the first variable. Mathematically a solution is simply a pair of points that make a series of equations true. Graphically represented, a solution is a series of points where the lines of the equations intersect.
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