Question

For the linear equation, find the product of 5 and the linear equation, and solve both equations for y. 2x + 7y = 11

Answer 1

Answer:

(a) $10x + 35y = 55$

(b) $y = \frac{11 - 2x}{7}$

Step-by-step explanation:

Given

$2x + 7y = 11$

Solving (a): Multiply equation by 5.

Multiply both sides by 5

$5 * (2x + 7y) = 11*5$

Open bracket

$5 * 2x + 5 * 7y = 11*5$

$10x + 35y = 55$

(b) Solve for y in $10x + 35y = 55$ and $2x + 7y = 11$

$10x + 35y = 55$

Subtract 10x from both sides

$35y = 55 - 10x$

Divide both sides by 35

$\frac{35y}{35} = \frac{55 - 10x}{35}$

$y = \frac{55 - 10x}{35}$

Factorize the numerator:

$y = \frac{5(11 - 2x)}{35}$

Express 35 as 7 * 5

$y = \frac{5(11 - 2x)}{7 * 5}$

$y = \frac{(11 - 2x)}{7}$

$y = \frac{11 - 2x}{7}$

When $2x + 7y = 11$ is solved, the solution will be: $y = \frac{11 - 2x}{7}$