Question

Write system of equations with the solution (1,3)​

Answer 1

To create a system with the solution (1,3), choose coefficients for two linear equations which, when solved, yield the solution (1,3). A valid example would be the system: y = 2x + 1 and y = x + 2. Verify by substituting (1,3) into both equations to ensure they are satisfied.

Step-by-step explanation:

To write a system of equations with the solution (1,3), you must create two linear equations where the point (1,3) is a solution to both equations. This means that if we substitute x with 1 and y with 3 in both equations, the equations should be true.

First, you may start by choosing arbitrary coefficients for x and y that, when applied to the solution (1,3), will result in a true statement. For example:

1. Let the first linear equation be y = mx + b. If we choose m=2 and b=1, the equation becomes y = 2x + 1. Substituting x and y with 1 and 3, respectively, gives us 3 = 2(1) + 1, which is true since both sides equal 3.
2. For the second equation, we could choose a different set of coefficients, say m=1 and b=2, resulting in the equation y = x + 2. Substituting again, we get 3 = 1(1) + 2, which is also true.

Therefore, the system of equations:

• y = 2x + 1
• y = x + 2

has the solution (1,3). We can enter the data into a calculator or compute it manually; either way, the coefficients are adjusted to validate the solution.

Following the steps mentioned in the provided information, we would:

• Identify the equation to use and write it down.
• Ensure that all values are in the correct units.
• Substitute the known quantities, along with their units, into the appropriate equation and obtain numerical solutions complete with units.
• Check the answer to see if it is reasonable by confirming that substituting the solution (1,3) into both equations satisfies them.