Question

How do you solve this system of equations: \[9y=3x+18\] and \[13x-y=-2\]?

Answer 1

Hint: This question belongs to the topic of algebra. For solving this question, we will use elimination methods. Using elimination method, we will multiply any one of the equations by a constant so that after adding or subtracting the equations, we will get the value of any one variable. After getting the value of any one variable, we will find the value of another variable.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to solve the system of two equations. The equations are \[9y=3x+18\] and \[13x-y=-2\]. From these equations, we have to find the value of x and y.
On multiplying the equation \[13x-y=-2\] by 9 on both sides, we get
\[\left( 13x-y \right)\times 9=-2\times 9\]
The above equation can also be written as
\[\Rightarrow 117x-9y=-18\]
Now, adding the above equation with the other equation that is \[9y=3x+18\], we will get
\[\left( 117x-9y \right)+\left( 9y \right)=\left( -18 \right)+\left( 3x+18 \right)\]
The above equation can also be written as
\[\Rightarrow 117x-9y+9y=-18+18+3x\]
The above equation can also be written as
\[\Rightarrow 117x=3x\]
The above equation can also be written as
\[\Rightarrow 117x-3x=0\]
The above equation can also be written as
\[\Rightarrow 114x=0\]
Hence, from the above equation we can say that x=0.
Now, putting this value of x as 0 in the equation \[9y=3x+18\], we get
\[9y=3\times 0+18\]
The above equation can also be written as
\[\Rightarrow 9y=18\]
From the above equation, we get that the value of y is 2.
Hence, the solution to the system of equations are x=0 and y=2.

Note: We should have a very deep knowledge in the topic of algebra for solving this type of question. Always remember that whenever we are going to solve two equations using elimination methods, then we will make coefficients of x or y same in both the equations by multiplying a constant to any of the equations. From there, we will get the value of y or x. For the value of x or y, we will put the value of y or x in any of the equations.