Answer:
To solve the system of equations by elimination, we need another equation that also includes the variables x and y.
Let's say we have the second equation as follows:
2x + 3y = 5
Now we will use the elimination method:
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations opposite of each other.
3(3x - 2y) = 3*3
2(2x + 3y) = 2*5
9x - 6y = 9
4x + 6y = 10
Now, add the two equations together:
(9x - 6y) + (4x + 6y) = 9 + 10
9x - 6y + 4x + 6y = 19
(9x + 4x) + (-6y + 6y) = 19
13x + 0y = 19
13x = 19
Divide both sides of the equation by 13:
13x/13 = 19/13
x = 19/13
Now, substitute this value of x into any of the original equations to find the value of y.
Let's use the first equation:
3x - 2y = 3
3(19/13) - 2y = 3
(57/13) - 2y = 3
Now, rearrange the equation to solve for y:
-2y = 3 - 57/13
-2y = 39/13 - 57/13
-2y = -18/13
Divide both sides of the equation by -2:
(-2y)/-2 = (-18/13)/-2
y = 18/13
Therefore, the solution to the system of equations is:
x = 19/13 and y = 18/13.