Answer: (0,3)
x=0 ; y=3
Explanation:
To solve the system of equations:
2x + 4y = 12
3x + y = 3
We can use the method of substitution or elimination. Here we will use the substitution method:
From Equation 2, we can isolate y:
y = 3 - 3x
We can substitute this expression for y into Equation 1:
2x + 4(3 - 3x) = 12
Simplifying and solving for x:
2x + 12 - 12x = 12
-10x = 0
x = 0
Now that we have found the value of x, we can substitute it back into either Equation 1 or Equation 2 to solve for y. Here we will use Equation 2:
3(0) + y = 3
y = 3
Therefore, the solution to the system of equations is (x, y) = (0, 3).
This means that the point (0, 3) is the intersection point of the two lines represented by the given equations. To verify this, we can substitute the values of x and y into both equations and see if they are true.