Question

Solve the following system of equations by the elimination method:

5x + 4y = –13, x – 2y = 3

Answer 1

Given system of equations:

5x + 4y = –13

x – 2y = 3

Step 1: Multiply the second equation by 4 to make the coefficients of (y) in both equations numerically equal but opposite in sign: 

4(x – 2y) = 4 × 3

⇒ 4x – 8y = 12

Our system becomes:

5x + 4⁢y = –13

4x – 8y = 12

Step 2: Now multiply the first equation by 2:

2(5x + 4y) = 2 × (–13) 

⇒ 10x + 8y = –26

Our system is now:

10x + 8y = –26 

4x – 8y = 12

Step 3: Add the two equations to eliminate (y):

(10x + 8y) + (4x – 8y) = –26 + 12

⇒ 14x = –14

Step 4: Solve for (x):

14x = –14

⇒ `x = (-14)/(14)`

⇒ x = –1

Step 5: Substitute (x = –1) into the second original equation:

x – 2y = 3

⇒ –1 – 2y = 3 

⇒ –2y = 3 + 1

⇒ –2y = 4

⇒ `y = (-4)/(2)`

⇒ y = –2

Thus, the solution to the system is x = –1 and y = –2.