Solving a System of Linear Equations: 24x + y = 48, 6x + y = 72

Math Problem Statement

answer

24x + y = 48, 6x + y = 72. The solution to the given system of equations is (x, y). What is the value of y?

We are given the following system of linear equations:

1) \ 24x + y &= 48 \\ 2) \ 6x + y &= 72 \end{aligned}$$ To find the value of $$y$$, we can solve this system step-by-step. ### Step 1: Subtract the second equation from the first. We'll eliminate $$y$$ by subtracting equation (2) from equation (1): $$(24x + y) - (6x + y) = 48 - 72$$ Simplifying: $$24x - 6x + y - y = -24$$ This reduces to: $$18x = -24$$ ### Step 2: Solve for $$x$$. $$x = \frac{-24}{18} = -\frac{4}{3}$$ ### Step 3: Substitute $$x = -\frac{4}{3}$$ into one of the original equations. We can substitute this value of $$x$$ into equation (2): $$6x + y = 72$$ Substituting $$x = -\frac{4}{3}$$: $$6\left(-\frac{4}{3}\right) + y = 72$$ Simplifying: $$-8 + y = 72$$ ### Step 4: Solve for $$y$$. $$y = 72 + 8 = 80$$ Thus, the value of $$y$$ is $$\boxed{80}$$. Would you like more details on any step, or do you have other questions? Here are 5 related questions to further explore this topic: 1. What is the value of $$x$$ in this system? 2. How can you verify the solution to a system of linear equations? 3. What methods other than substitution can solve systems of linear equations? 4. How can graphing be used to solve this system of equations? 5. What happens when a system of equations has no solution or infinitely many solutions? **Tip**: In systems of equations, subtracting or adding the equations to eliminate a variable can be a quick way to solve for the remaining variable.

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Linear Equations
Systems of Equations
Substitution Method
Elimination Method

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