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How do you solve for y: $2x - 4y = 6$ ?

Last updated date: 15th Jun 2024
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Hint: In this question, we are given an expression containing two unknown variable quantities, so it is an algebraic expression. Arithmetic operations like addition, subtraction, multiplication and division are used to link the numerical values with the alphabets, and the alphabets represent some unknown quantities. We know that we need the “n” number of equations to find the value of “n” unknown variables. In the given algebraic expression, we have 2 unknown quantities but only one equation to solve them so we can’t find the value of any variable from this equation. We have to solve for y so we will express y in terms of x. For that, we will rearrange the equation such that y lies on the one side of the equation and all other terms lie on the other side. We will obtain an expression in which y will lie on one side and the other side will contain x and some constant terms.

Complete step-by-step solution:
We are given that $2x - 4y = 6$
To solve for the value of y, we take 2x and -4 to the right-hand side –
   - 4y = 6 - 2x \\
   \Rightarrow y = \dfrac{{ - 1}}{4}(6 - 2x) \\
   \Rightarrow y = \dfrac{x}{2} - \dfrac{3}{2} \\
Hence, when $2x - 4y = 6$ , we get $y = \dfrac{x}{2} - \dfrac{3}{2}$

Note: By putting different values of x and then solving the equation, we can find the values of y. The given equation is also known as a linear equation. We can also graph the given equation by putting different values of “x” in the given equation and getting the value of “y”. Thus, we can also use the equation for plotting the graph of this straight line.