Question

Solve the following system of equations by the elimination method:

3x = 4 – 5y, 2x – y = 7

Answer 1

Given: 3x = 4 – 5y, 2x – y = 7

Step 1: Rewrite the first equation in standard form

From the first equation:

3x = 4 – 5y

⇒ 3x + 5y = 4

So our system is 3x + 5y = 4, 2⁢x – y = 7.

Step 2: Eliminate one variable

To eliminate (y), multiply the second equation by 5 so coefficients of (y) become (5) and (–5):

5(2x – y) = 5 × 7 

⇒ 10x – 5y = 35

Now the system is 3x + 5y = 4, 10x – 5⁢y = 35.

Add both equations:

(3x + 5y) + (10x – 5y) = 4 + 35 

3x + 10x + 5y – 5y = 39 

13x = 39

`x = 39/13`

x = 3

Step 3: Substitute (x = 3) into one of the equations

Use the second equation:

2x – y = 7 

⇒ 2(3) – y = 7

⇒ 6 – y = 7 

⇒ –y = 7 – 6

⇒ –y = 1 

⇒ y = –1

The solution to the system is x = 3, y = –1.