Question

Create a system of linear equations that has one solution.

Answer 1

Please check the explanation.

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

In order to create the system of linear equations that has one solution, we need to have two linear equations with different slopes

Let the linear system of equation with different slopes be

y = 5x + 4

y = 4x + 3

comparing with the slope-intercept form (y = mx+b) of line/linear equation

Here,

y = 5x + 4 has the slope m = 5

y = 4x + 3 has the slope m = 4

solving the system of equations using the elimination method

`\begin{bmatrix}y=5x+4\\ y=4x+3\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y-5x=4\\ y-4x=3\end{bmatrix}`

subtracting the equations

`y-4x=3`

`-`

`\underline{y-5x=4}`

`x=-1`

For y-5x=4 plug in x=-1

`y-5\left(-1\right)=4`

`y+5=4`

subtract 5 from both sides

`y+5-5=4-5`

Simplify

`y=-1`

Therefore, the one solution to the system of equations is:

`y=-1,\:x=-1`