Answer:
(0,3)
Explanation:
To solve the system of equations:
2x + 4y = 12
3x + y = 3
We can use the substitution method or the elimination method. Let's use the elimination method to solve this system.
To eliminate the y term, we'll multiply equation 2) by 4:
4(3x + y) = 4(3)
12x + 4y = 12
Now we have the system of equations:
2x + 4y = 12
12x + 4y = 12
Subtract equation 1) from equation 3) to eliminate the y term:
(12x + 4y) - (2x + 4y) = 12 - 12
12x + 4y - 2x - 4y = 0
10x = 0
x = 0
Now substitute x = 0 into equation 2) to find y:
3(0) + y = 3
y = 3
Therefore, the solution to the system of equations is x = 0 and y = 3.
To check the solution, we can substitute x = 0 and y = 3 into the original equations:
2(0) + 4(3) = 12
0 + 12 = 12 (True)
3(0) + 3 = 3
0 + 3 = 3 (True)
So, the solution (0, 3) satisfies both equations.