Question

Solve by elimination: 3x + y = 7 and -x + 2y = 0.

Answer 1

You have the following system of equations:

3x + y = 7 (1)

-x + 2y = 0 (2)

In order to solve the previous system by elimination, you proceed as follow:

first, multiply the second equation by 3:

(-x + 2y = 0)(3)

-3x + 6y = 0

next, you sum the last equation with the first equation

3x + y = 7

-3x + 6y = 0

0 + 7y = 7

From the last equation, you solve for y:

7y = 7 divide by 7 both sides

y = 7/7

y = 1

next, you replace the value of y in one of the equation of the system, say in the equation (2) and solve for x:

-x + 2y = 0

-x + 2(1) = 0

-x + 2 = 0 add 2 both sides

x = 2

Hence, the solution to the given system of equations is:

x = 2

y = 1