Question

How do you solve \[9x-3y=3\ and\ 3x+8y=-17\] ?

Answer 1

Hint: In the given question, we have been asked to solve a system of equations i.e. \[9x-3y=3\ and\ 3x+8y=-17\]. In order to solve the equations we will use elimination methods. We need to either add both the equations or subtract both the equations to get the equation in one variable. Then we solve the equation in one variable in a way we solve the general linear equation.

Complete step by step answer:
We have given that
\[9x-3y=3\]------ (1)
\[\Rightarrow 3x+8y=-17\]----- (2)
Multiply the equation (2) by 3, we get
\[9x+24y=-51\]----- (3)
Subtracting equation (3) from equation (1), we get
\[9x-3y-9x-24y=3-\left( -51 \right)\]
Combining the like terms, we get
\[-27y=3-\left( -51 \right)\]
Simplifying the numbers in the above equation, we get
\[-27y=54\]
Dividing both the sides of the equation by -27, we get
\[y=-2\]
Substitute the value of \[y=-2\] in equation (1), we get
\[9x-3y=3\]
\[\Rightarrow 9x-3\times \left( -2 \right)=3\]
\[\Rightarrow 9x+6=3\]
Subtracting \[6\] from both the sides of the equation, we get
\[\Rightarrow 9x+6-6=3-6\]
Simplifying the numbers in the above equation, we get
\[ 9x=-3\]
Dividing both the side of the equation by 9, we get
\[ x=-\dfrac{1}{3}\]
Therefore, we get \[\left( x,y \right)=\left( -\dfrac{1}{3},-2 \right)\]

Therefore, the possible value of ‘x’ and ‘y’ is\[\left( x,y \right)=\left( -\dfrac{1}{3},-2 \right)\].

Note:In an elimination method for solving a system of equations we will either add both the equations or subtract both the equations to get the equation in one variable. To eliminate the variable, you will add the two given equations if the coefficients of one variable are opposites and you will subtract the two equations if the coefficient of one variable is exactly the same. If both the situations do not satisfy then we will need to multiply one of the equations by a number that will lead to the same leading coefficient.