Answer:
(a) [tex]10x + 35y = 55[/tex]
(b) [tex]y = \frac{11 - 2x}{7}[/tex]
Step-by-step explanation:
Given
[tex]2x + 7y = 11[/tex]
Solving (a): Multiply equation by 5.
Multiply both sides by 5
[tex]5 * (2x + 7y) = 11*5[/tex]
Open bracket
[tex]5 * 2x + 5 * 7y = 11*5[/tex]
[tex]10x + 35y = 55[/tex]
(b) Solve for y in [tex]10x + 35y = 55[/tex] and [tex]2x + 7y = 11[/tex]
[tex]10x + 35y = 55[/tex]
Subtract 10x from both sides
[tex]35y = 55 - 10x[/tex]
Divide both sides by 35
[tex]\frac{35y}{35} = \frac{55 - 10x}{35}[/tex]
[tex]y = \frac{55 - 10x}{35}[/tex]
Factorize the numerator:
[tex]y = \frac{5(11 - 2x)}{35}[/tex]
Express 35 as 7 * 5
[tex]y = \frac{5(11 - 2x)}{7 * 5}[/tex]
[tex]y = \frac{(11 - 2x)}{7}[/tex]
[tex]y = \frac{11 - 2x}{7}[/tex]
When [tex]2x + 7y = 11[/tex] is solved, the solution will be: [tex]y = \frac{11 - 2x}{7}[/tex]
