Question

Create a system of linear equations that has one solution, Solve the system using

elimination to prove your that your system has only one solution

Answer 1

To create and solve a system of linear equations with one solution by elimination, we can set up two intersecting lines such as y = 2x + 3 and y = -x - 1, and eliminate variables to find the single point of intersection, which in this case is (x, y) = (-4/3, 1/3).

Step-by-step explanation:

To create a system of linear equations that has one solution and prove its uniqueness by solving with elimination, we can consider two equations that intersect at exactly one point. For instance

• Equation 1: y = 2x + 3
• Equation 2: y = -x - 1

To solve by elimination, we can multiply the second equation by 2 to match the coefficient of x in the first equation:

• Equation 2 modified: 2y = -2x - 2

Add Equation 1 and the modified Equation 2 to eliminate the y variable:

• 3y = 1

Now, solve for y:

• y = 1/3

Substituting y = 1/3 into Equation 1:

• 1/3 = 2x + 3
• 2x = -8/3
• x = -4/3

Thus, the solution to the system is (x, y) = (-4/3, 1/3), which proves that the system has only one solution.

Answer 2

equation 1: 4y+2x= 4
equation 2: 4y+6x=8

4y+2x=4
-
4y+6x=8
—————
-4x=-4
x=1

plug back in 4y+2=4
4y=2

y=1/2

solution at (1, 1/2 )