1.) Write a system of equations that has NO solution.
2.) If you wanted to eliminate the y variables in the system of equations below, what would you multiply the first and second equations by?( Do not solve the equation) 2x-3y=8
7x-4y=11
Can't anyone help me with these problems?:(
1.) To create a system of equations that has no solution, we can set up two equations with parallel lines. For example:
- Equation 1: 2x - 3y = 4
- Equation 2: 4x - 6y = 8
2.) To eliminate the y variables in the given system of equations:
- Equation 1: 2x - 3y = 8
- Equation 2: 7x - 4y = 11
We can multiply the first equation by 4 and the second equation by 3 to obtain coefficients that will cancel out the y variables when both equations are added.
1.) To create a system of equations with no solution, we need to ensure that the equations are inconsistent, meaning that they cannot be true at the same time. One way to do this is by setting the coefficients of the variables to be proportional in one equation, but not in the other.
For example:
Equation 1: 2x + 3y = 8
Equation 2: 4x + 6y = 16
In this system, Equation 2 can be obtained by doubling the coefficients of Equation 1. Therefore, the equations are proportional, and this system has no solution.
2.) To eliminate the y variables in the system of equations, we can use the method of elimination. This requires multiplying either or both equations by a constant to have coefficients of y in both equations that are additive inverses of each other.
Looking at the given system:
Equation 1: 2x - 3y = 8
Equation 2: 7x - 4y = 11
We can eliminate the y variables by multiplying Equation 1 by 4 and Equation 2 by 3. This will give us new coefficients for y that are the additive inverses of each other:
Multiplying Equation 1 by 4:
4(2x - 3y) = 4(8)
8x - 12y = 32
Multiplying Equation 2 by 3:
3(7x - 4y) = 3(11)
21x - 12y = 33
By multiplying Equation 1 by 4 and Equation 2 by 3, the new coefficients for y are -12 and -12 respectively. These coefficients are additive inverses, allowing us to eliminate the y variables when we add or subtract the two equations.