What is the Solution to the following set of equations

Question

2x+4y = 16 & 3x - y = 9?

Answer 1

Substitution Method :

The system of equations are 2x + 4y = 16 and 3x - y = 9.

Step 1 : Solve the equation 2 : 3x - y = 9 for y since the coefficient is negative 1.

Subtract 3x from each side.

3x - y - 3x = 9 - 3x

- y = 9 - 3x

Multiply each side by negative 1.

y = - 9 + 3x

 

Step 2 : Substitute - 9 + 3x for y in the equation 1 : 2x + 4y = 16 to find the value of x.

2x + 4(- 9 + 3x) = 16

Apply distributive property : a(b + c) = ab + ac.

2x - 36 + 12x = 16

14x - 36 = 16

Add 36 to each side.

14x - 36 + 36 = 16 + 36

14x = 52

Multiply each side by 14.

x = 52/14 = 26/7.

 

Step 3 : Substitute 26/7 for x in either equation to find y.

Equation 2 : 3x - y = 9.

3(26/7) - y = 9

78/7 - y = 9

y = 78/7 - 9 = [ 78 - 7(9) ]/7 = [ 78 - 63 ]/7 = 15/7.

 

The solution is (26/7, 15/7).