# Solve the following equations: x + 8y = 19 and 3x - y = 4

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The set of linear equations

x + 8y = 19 ...(1)

3x - y = 4 ...(2)

has to be solved for x and y

From (1)

x = 19 - 8y

Substitute in (2)

=> 3(19 - 8y) - y = 4

=> 57 - 24y - y = 4

=> 53 = 25y

=> y = 53/25

x = 51/25

**The solution of the set of equations is x = 51/25, y = 53/25**

X + 8Y = 19 ...(1)

3X - Y = 4 ...(2)

multiply the second equation by 8

8 x (2) => 24X - 8Y = 32 ....(3)

add the first and third equations

(1)+(3)=> X + 8Y +24X -8Y = 19 + 32

=> 25X =51

=> **X = 51/25 **

Substitute this value in the second equation

=> 3X - Y = 4

=>3 (51/25) - Y = 4

=> Y = 3(51/25) -4

=> Y = (153/25) - 4

=> Y = (153/25) - (100/25)

=>**Y = 53/25**

x + 8y = 19

3x - y = 4

First, multiply everything in the first equation by 3

By multiplying, your equation should look like

**3x + 24y = 57 **

**3x - y = 4 **now, subtract 3x with 3x ( which means subtract 24y with " y " and 57 with 4 )

By subtracting, your equation should look like

**25y = 53 **now divide both sides by 25

By dividing, your equation should look like

**y = 53/25 **which is your answer for " y "

Now, plug 53/25 into one of the equation

**3x - 53/25 = 4 **add 53/25 on both sides

By adding, your equation should look like

**3x = 153/25 **now divide both sides by 3

By dividing, your equation should look like

**x = 51/25 **which is your answer for " x "

So your answer is **x = 51/25 ; y = 53/25**

(a) x + 8y = 19

(b) 3x - y = 4

1. (c) = Multiply (b) by 8:

24x - 8y = 32

2. Add (a) and (c)

24x - 8y = 32

+

x + 8y = 19

-------------------------

25x = 51 ---> x = 51/25

3. Plug in this x value into equation (a) or (b) and solve for y.