solve by elimination method.
2x+3y=4
4x+6y=8
is the answer -3/2y+2
they want it as an ordered pair
No. Both equations describe the same line. An ordered pair is an answer of (3,2) where 3 is the x value and 2 is the y value. But in this case the lines don't intersect and there are an infinite number of solutions. Check my thinking.
DrWLS gave you the same answer.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply either equation by a constant to make the coefficients of one of the variables the same in both equations. In this case, we can multiply the first equation by 2 to make the coefficient of x the same in both equations:
Equation 1: 2(2x + 3y) = 2(4)
4x + 6y = 8
Equation 2: 4x + 6y = 8
Step 2: Subtract one equation from the other to eliminate one variable. In this case, we'll subtract Equation 2 from Equation 1:
(4x + 6y) - (4x + 6y) = 8 - 8
0 = 0
As a result, we end up with a true statement (0 = 0), indicating that the two equations are actually equivalent and that there are infinitely many solutions. In this case, the two equations define the same line.
Therefore, if you try to solve for x or y, you would end up with a variable that cancels out, leaving no unique solution. The system of equations is dependent, meaning that any value you assign to one variable will determine the other variable.
As a result, the answer cannot be expressed as a single ordered pair. You can choose any value for one variable, solve for the other variable, and write the solutions as ordered pairs.
For example, if we choose a value for x, let's say x = 0, the second equation becomes:
4(0) + 6y = 8
6y = 8
y = 8/6
y = 4/3
Therefore, one possible solution is (x, y) = (0, 4/3). However, you can choose any value for x and find the corresponding value for y to get different ordered pairs.