# What is the y-value of the solution to the system of equations?

3x + 5y = 1; 7x + 4y = - 13

**Solution:**

**Step 1:**

Given system of equations are

3x + 5y = 1 --- (1)

7x + 4y = -13 --- (2)

By using the elimination method

**Step 2:**

We can eliminate either x or y

x term can be eliminated by multiplying equation (1) with 7 and equation (2) with 3

3x + 5y = 1 --- (1) × 7

7x + 4y = - 13 --- (2) × 3

⇒ 21x + 35 y = 7

21x + 12y = -39

**Step 3:**

On subtracting both the equations

⇒ 21x + 35 y = 7

21x + 12y = -39

⇒ (21- 21) x + (35 - 12)y = (7+39)

⇒ 23y = 46

⇒ y = 46/23 = 2

**Step4:**

Substitute now the value of y = 2 in any of the equations (1) and (2)

Substituting the value of y=2 in equation (1)

⇒ 3x + 5(2) = 1

⇒ 3x + 10 = 1

⇒ 3x = 1 - 10

⇒ 3x = -9

⇒ x = - 9/3

⇒ x = -3

## What is the y-value of the solution to the system of equations?

3x + 5y = 1

7x + 4y = - 13

**Summary: **

The y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.