Question

Write a system of equations that satisfies each condition below: One solution at (4,5) The y-intercept of one of the equations is 3. The other equation is not written in slope-intercept form

Answer 1

`\begin{gathered} y-(1)/(2)x=3 \\ y-x=1 \end{gathered}`

Explanation:

The first thing is to raise the system of equations to add the conditions mentioned in the statement

We use an equation in the slope-intercept form and another in its slope-point form

`\begin{gathered} y=mx+b \\ y-y_1=m\cdot(x-x_1) \end{gathered}`

now, replacing

One solution is (4,5), so those are the values of x1 and y1.

The y-intercept is equal to 3, therefore b = 3

The slope is calculated like this

`\begin{gathered} y=mx+b \\ 5=m\cdot4+3 \\ 4m=5-3 \\ m=(2)/(4) \\ m=(1)/(2) \end{gathered}`

replacing, the another slope is 1

`\begin{gathered} y=(1)/(2)(x+3)\rightarrow y=(1)/(2)x+3\rightarrow y-(1)/(2)x=3 \\ y-5=x-4\rightarrow y-x=-4+5\rightarrow y-x=1 \end{gathered}`