Answer:
the solution to the system is (x, y) = (17/9, 0).
Explanation:
To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the two equations. The goal is to end up with a single equation in one variable, which we can then solve for that variable. Then, we can substitute the value we found back into one of the original equations to solve for the other variable.
Here are the steps to solve the system:
Rearrange the equations in standard form, which means putting all the variables on one side and all the constants on the other side:
12y + 9x = 17
-4y - 3x = 31
Multiply the second equation by 3 to get the coefficients of x to be opposite:
12y + 9x = 17
-12y - 9x = 93
Add the two equations to eliminate x:
0y = 110
This equation is true for all values of y, which means there are infinitely many solutions to the system. However, the system does not have a unique solution because the two equations are dependent and represent the same line. Therefore, any point that satisfies one of the equations also satisfies the other equation.
To find a solution, we can pick a value for y and then solve for x. For example, let's choose y = 0. Then, from the first equation, we get:
12(0) + 9x = 17
9x = 17
x = 17/9
So one solution to the system is (x, y) = (17/9, 0). We can check that this solution satisfies both equations:
12(0) + 9(17/9) = 17
-4(0) - 3(17/9) = 31
Therefore, the solution to the system is (x, y) = (17/9, 0).