Final answer:
To solve the system of equations using elimination, we can multiply one or both equations by a constant to eliminate one variable. In this case, multiplying the first equation by 5 and the second equation by 3 allows us to eliminate the x variable. Solving for y and substituting the value back into one of the equations gives us the solution x = 3.33 and y = 4.
Step-by-step explanation:
To solve the system of equations using elimination, we need to eliminate one variable by multiplying one or both equations by a constant so that the coefficients of either x or y will be the same.
Let's multiply the first equation by 5 and the second equation by 3:
15x - 10y = 10
15x - 15y = 30
Now, subtract the second equation from the first equation:
(15x - 10y) - (15x - 15y) = 10 - 30
Simplify the equation:
-5y = -20
Divide both sides of the equation by -5 to solve for y:
y = 4
Next, substitute the value of y into one of the original equations, such as the first equation:
3x - 2(4) = 2
Simplify the equation:
3x - 8 = 2
Add 8 to both sides of the equation:
3x = 10
Divide both sides of the equation by 3 to solve for x:
x = 10/3 = 3.33
Therefore, the solution to the system of equations is x = 3.33 and y = 4.