Answer

Verified

341.4k+ views

**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,

\[

2x - 2x + y = 10 - 2x \\

\Rightarrow 0 + y = 10 - 2x \\

\Rightarrow y = 10 - 2x \;

\]

Now substituting \[10 - 2x\] for “y” in the second equation and solving for “x” we have,

\[5x - \left( {10 - 2x} \right) = 18\]

Expanding the brackets by multiplying the negative sign we have,

\[

\Rightarrow 5x - 10 + 2x = 18 \\

\Rightarrow 7x - 10 = 18 \;

\]

Adding \[10\] both the sides in left hand side and right hand side we have,

\[

7x - 10 + 10 = 18 + 10 \\

\Rightarrow 7x - 0 = 28 \\

\Rightarrow 7x = 28 \;

\]

Dividing by \[7\] ,

\[ \Rightarrow \dfrac{{7x}}{7} = \dfrac{{28}}{7}\]

Cancelling \[7\] and dividing \[7\] by \[28\] ,

\[ \Rightarrow x = 4\]

Now substituting \[4\] for “x” in the solution to the first equation and calculating for “y” we have,

\[

y = 10 - \left( {2 \times 4} \right) \\

\Rightarrow y = 10 - 8 \\

\Rightarrow y = 2 \;

\]

**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.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE