solve 12y=17-9x using the elimination method
there is no second equation to use for elimination.
To solve the equation 12y = 17 - 9x using the elimination method, we need to eliminate one variable (either x or y) by manipulating the equation. Here's how you can do it step-by-step:
Step 1: Write down the equation: 12y = 17 - 9x.
Step 2: Rearrange the equation so that the terms containing the variable are next to each other:
-9x - 12y = -17
Step 3: Now, let's choose a way to eliminate one variable. In this case, we can eliminate the x variable by multiplying the entire equation by -1, which will reverse the sign of every term.
-(-9x) - (-12y) = -(-17)
9x + 12y = 17
Step 4: Now, you have two equations:
-9x - 12y = -17 (equation from Step 2)
9x + 12y = 17 (equation from Step 3)
Step 5: Add the two equations together. Since the -12y and 12y terms have opposite signs, when we add them, they cancel out.
(-9x - 12y) + (9x + 12y) = -17 + 17
-9x + 9x + 0y = 0
Step 6: Simplify the equation. The variables have been eliminated, and we are left with 0y, which simplifies to 0.
0 = 0
Step 7: Interpret the result. The equation 0 = 0 is a true statement, which means that the original equation 12y = 17 - 9x is true for all values of x and y. This implies that there are infinitely many solutions to the original equation.
Therefore, the solution to the equation 12y = 17 - 9x using the elimination method is any point (x, y) that satisfies the equation.