Solve the system of equations

Question

x - 4y = 33

6x - 7y = 14

Answer 1

Substitution Method :

The system of equations are x - 4y = 33 and 6x - 7y = 14.

Step 1 : Solve the equation 1 : x - 4y = 33 for x since the coefficient is 1.

Add 4y to each side.

x - 4y + 4y = 33 + 4y

x = 33 + 4y

 

Step 2 : Substitute 33 + 4y for x in the equation 2 : 6x - 7y = 14 to find the value of y.

6(33 + 4y) - 7y = 14

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

198 + 24y - 7y = 14

198 + 17y = 14

Subtract 198 from each side.

198 + 17y - 198 = 14 - 198

17y = - 184

Divide each side by 17.

y = - 184/17.

 

Step 3 : Substitute - 184/17 for y in either equation to find x.

Equation 1 :x - 4y = 33

x - 4(- 184/17) = 33

x + 736/17 = 33

x = 33 - 736/17 = [ (33)(17) - 736 ]/17 = (561 - 736)/17 = - 175/17.

 

The solution is (- 175/17, - 184/17) ≅ (- 10.294, - 10.824).