Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 04, 2024

Find the value of $y$ given the linear equation $2x + 5y = 10$ .

STEP 1

Assumptions
1. We have a linear equation in two variables, $x$ and $y$ .
2. The equation is $2x + 5y = 10$ .
3. We need to solve for $y$ in terms of $x$ .

STEP 2

Isolate the term containing $y$ by moving all other terms to the other side of the equation.
$5y = 10 - 2x$

STEP 3

Divide both sides of the equation by the coefficient of $y$ to solve for $y$ .
$y = \frac{10 - 2x}{5}$

STEP 4

Simplify the right side of the equation by dividing each term inside the numerator by 5.
$y = \frac{10}{5} - \frac{2x}{5}$

STEP 5

Complete the simplification to find the expression for $y$ .
$y = 2 - \frac{2}{5}x$
So the solution for $y$ in terms of $x$ is $y = 2 - \frac{2}{5}x$ .

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