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How do you solve \[y = 4x - 3,2y - 3x = 4\] ?

seo-qna
Last updated date: 23rd Feb 2024
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IVSAT 2024
Answer
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Hint: This question is from the topic solution of linear system of equations in two variables. In this question we have to solve the system of linear equations \[y = 4x - 3,2y - 3x = 4\]. We solve for systems of linear equations of two variables by elimination method, substitution method or graphing method. Elimination method is the easiest method for finding a solution of a linear system of equations in two variables.

Complete step by step solution:
Let us try to solve this question in which we are asked to find the solution of the linear system of equations in two variables formed by \[y = 4x - 3,2y - 3x = 4\]. We are using elimination methods for finding the solution. In elimination method for solving linear equation of two variables by eliminating one variable by equaling it in both equations and after cancellation we get equation in one variable, finally simply solve it. Let’s apply the elimination method given the system of linear equations \[y = 4x - 3,2y - 3x = 4\]. We have
\[y = 4x - 3,2y - 3x = 4\]
Can be written as follows, $4x - y = 3$ and the other equation as follows $ - 3x + 2y = 4$.
As per the steps of elimination method, we will eliminate variable $y$ by equating the coefficient of $y$ in both equations. In equation $4x - y = 3$ we have coefficient of $y$ equals $ - 1$ and coefficient of $y$ in equation $ - 3x + 2y = 4$ is $2$.
To eliminate variable $y$ we multiply equation $4x - y = 3$by$2$.
Multiplying equation $4x - y = 3$ by $2$, we get
$8x - 2y = 6$ $----eq(1)$
$ - 3x + 2y = 4$------ $eq(2)$
Now adding both equations $eq(1)$ and $eq(2)$, we get
$5x = 10$ --------$eq(3)$
Now dividing both sides of $eq(3)$ by $5$, we get the value of $x$.
$x = 2$
Now putting back the value of $x$ in $eq(2)$ to get the value of $y$
$
- 3x + 2y = 4 \\
- 3 \cdot (2) + 2y = 4 \\
2y = 10 \\
y = 5 \\
$
Hence the solution of the linear system of equations \[y = 4x - 3,2y - 3x = 4\] is $x = 2$ and $y = 5$.

Note: While solving these types of questions in which we are asked to find the solution of linear systems of equations in two variables students must be careful about the signs of variables and constant terms. We can also check the correctness of solutions by putting back the values of $x$ and $y$ in the given system of linear equations.