Final answer:
To solve the system of linear equations using elimination, we need to eliminate one variable by adding or subtracting the equations. By multiplying the second equation by 3 and subtracting the first equation, we can eliminate the y variable and solve for x. Substituting this value into any of the original equations, we can solve for y.
Step-by-step explanation:
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the equations so that we are left with one equation with one variable.
Multiplying the second equation by 3, we get 9x + 3y = 6.
Subtracting the first equation from this new equation, we eliminate the y variable: (9x + 3y) - (2x + 3y) = 6 - 0, which simplifies to 7x = 6.
Dividing both sides of the equation by 7, we get x = 6/7.
Substituting this value of x into any of the original equations, we can solve for y:
Using the second equation:
3(6/7) + y = 2
18/7 + y = 2
y = 2 - 18/7
y = -4/7
Therefore, the solution to the system of equations is (6/7, -4/7).