solve and check 2x+5y=38 and x-3y=-3

Question

2x+5y=38 and  x-3y=-3.

Answer 1

Substitution method :

The system of equations are 2x + 5y = 38 and x - 3y = - 3.

Solve the equation 2 : x - 3y = - 3 for x, since the x has a coefficient of 1.

x - 3y = - 3

x = 3y - 3.

Substitute the value of x = 3y - 3 in the equation 1: 2x + 5y = 38 and solve for y.

2(3y - 3) + 5y = 38

6y - 6 + 5y = 38

11y - 6 = 38

11y = 38 + 6

11y = 44

y = 44/11

y = 4.

Substitute the value of y = 4 in the equation x = 3y - 3 to find the value of x.

x = 3(4) - 3

x = 12 - 3

x = 9.

The solution is x = 9 and y = 4.

Check :

Substitute x = 9 and y = 4 in equation 2 : x - 3y = - 3.

9 - 3(4) = - 3

9 - 12 = - 3

- 3 = - 3.

The above statement is true, so (x, y) = (9, 4) is a solution of given system of equations.