x + y =3 , 3x-2y = 4 Identify the point of intersection

Question

What is the solution of the following system?

x + y = 3,

3x-2y = 4

Identify the point of intersection

Answer 1

Substitution method :

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

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

x + y = 3

y = 3 - x.

Substitute the value of y = 3 - x in the equation 2: 3x - 2y = 4 and solve for x.

⇒ 3x - 2(3 - x) = 4

⇒ 3x - 6 + 2x = 4

⇒ 5x - 6 = 4

⇒ 5x = 4 + 6

⇒ 5x = 10

⇒ x = 10/5

⇒ x = 2.

Substitute the value of x = 2 in the equation y = 3 - x to find the value of y.

⇒ y = 3 - 2

⇒ y = 1.

The intersection point is (x, y ) = (2, 1).