19x - 14y = 27
Understand the Problem
The question is asking for a solution to the linear equation in terms of x and y. We may need to rearrange or isolate one variable to solve for it.
Answer
For $y$: $y = \frac{c - ax}{b}$; for $x$: $x = \frac{c - by}{a}$
Answer for screen readers
For $y$ in terms of $x$: $y = \frac{c - ax}{b}$
For $x$ in terms of $y$: $x = \frac{c - by}{a}$
Steps to Solve
- Identify the linear equation
Assume the linear equation is given as $ax + by = c$, where $a$, $b$, and $c$ are constants.
- Isolate the variable
To solve for $y$, we'll rearrange the equation. Subtract $ax$ from both sides:
$$ by = c - ax $$
- Divide to solve for y
Now, divide both sides by $b$ to isolate $y$:
$$ y = \frac{c - ax}{b} $$
- Simplify if necessary
Check if this can be simplified further.
Now, if we wanted to solve for $x$, we'd rearrange the original equation differently:
- Move terms to isolate x
Subtract $by$ from both sides:
$$ ax = c - by $$
- Divide to solve for x
Then divide both sides by $a$:
$$ x = \frac{c - by}{a} $$
For $y$ in terms of $x$: $y = \frac{c - ax}{b}$
For $x$ in terms of $y$: $x = \frac{c - by}{a}$
More Information
These equations allow you to express one variable in terms of the other based on the linear relationship defined by the original equation. This is a fundamental skill in algebra that helps in solving many equations.
Tips
- Forgetting to invert the sign when moving terms across the equation.
- Mixing up the variables, especially if the coefficients are similar. Always double-check which variable you are solving for.
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