How do you solve this system of equations:
and ?
Answer
Verified
438.9k+ views
Hint: To solve such questions start by multiplying the second given equation with the number . Then subtract the first given equation from the other one which is multiplied by the number . Once the value of is found use that to find the value of .
Complete step by step answer:
Given the equations and .
It is asked to solve these equations.
Suppose that
And
Multiply both the LHS and RHS of the equation with the number , that is
Further computing we get,
Next, subtract the equation from the equation , that is
Further simplifying we get,
Dividing throughout by number , we get
That is we get
Now substitute the value of in equation , that is
Further simplifying, we get
That is,
Subtracting the RHS we get,
Therefore, the solution of the given system of equations is and .
Additional information:
An equation that can be written in the form , where , and are real numbers, and and are not both zero, is known as a linear equation in two variables and . Every solution of the equation is a point on the line representing it.
Note: These types of questions are easy to solve. There are different methods to solve linear equations with two variables, that is, method of substitution and method of elimination. In this solution part, we have used a method of elimination. One can check whether the obtained values of and is correct or not by putting those in the given equations.
Complete step by step answer:
Given the equations
It is asked to solve these equations.
Suppose that
And
Multiply both the LHS and RHS of the equation
Further computing we get,
Next, subtract the equation
Further simplifying we get,
Dividing throughout by number
That is we get
Now substitute the value of
Further simplifying, we get
That is,
Subtracting the RHS we get,
Therefore, the solution of the given system of equations is
Additional information:
An equation that can be written in the form
Note: These types of questions are easy to solve. There are different methods to solve linear equations with two variables, that is, method of substitution and method of elimination. In this solution part, we have used a method of elimination. One can check whether the obtained values of
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