Consider the following system of equations:
2x + 3y = 12 - 4x + 5y = 4
Which of the following equations could be used to create an equivalent system (a system with the same solution)? Select all the apply.
- 8x + 10y = - 4
- 2x + 8y = 8
6x + 9y = 36
6x - 2y = 8
x + 3/2 * y = 6
To create an equivalent system of equations, we can perform operations of adding, subtracting or multiplying each equation by a constant.
Let's look at each option:
- 8x + 10y = - 4: Multiplying by 2 gives 16x + 20y = -8, which is not equivalent to the given system.
- 2x + 8y = 8: Multiplying by 2 gives 4x + 16y = 16, which is not equivalent to the given system.
- 6x + 9y = 36: Multiplying by 1 gives the equation 6x + 9y = 36, which is the same as the first equation in the given system.
- 6x - 2y = 8: This equation doesn't match any of the equations in the given system.
- x + 3/2 * y = 6: Multiplying by 2 gives 2x + 3y = 12, which is the same as the first equation in the given system.
So, equations 6x + 9y = 36 and x + 3/2 * y = 6 could be used to create an equivalent system.