Question

How do you solve using elimination of $3x – 2y= -1$ and $3x – 4y = 9 ?$

Answer 1

Hint: We are given a system of 2 linear equations which have 2 unknown variables as $x$ and $y$. In the elimination method, first we will find the value of one variable, i.e. $x$ in terms of another variable, i.e. $y$. So, we will get $3x = 4y + 9$ from the first equation. Now, we will substitute it in the second equation and obtain the value of $y$. This value can be substituted in any of the equations to get the value of $x$.

Complete step by step solution:
The given equations are $3x – 2y= -1$ and $3x – 4y = 9$.
From the equation $3x – 4y = 9$, we can say 3x is equal to $4y + 9$. We can see that there is a term 3x in the equation $3x – 2y= -1$ we can replace the term $3x$ in the equation $3x – 2y= -1$.
So $4y + 9 – 2y= -1$
Further solving we get $2y + 9= -1$
Subtracting $9$ from both sides we get $2y = -10$
So $y$ is equal to $-5$
Now putting y equal to $-5$ in $3x – 4y=9$ we get $3x + 20 = 9$, so the value of $x$ is equal to $-\dfrac{11}{3}$. So $x= -\dfrac{11}{3}$ and $y= -5$ are the solution.

Note: We can also solve the equation by drawing the graph of the given 2 equations. We can draw the graph of both equations and the intersecting point will be the solution of the system of equations. In this case both equations will be a straight line and the intersecting point will be at $\left( -\dfrac{11}{3},-5 \right)$ .