Respuesta :
ANSWER:
[tex]\begin{gathered} y-\frac{1}{2}x=3 \\ y-x=1 \end{gathered}[/tex]STEP-BY-STEP 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
[tex]\begin{gathered} y=mx+b \\ y-y_1=m\cdot(x-x_1) \end{gathered}[/tex]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
[tex]\begin{gathered} y=mx+b \\ 5=m\cdot4+3 \\ 4m=5-3 \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]replacing, the another slope is 1
[tex]\begin{gathered} y=\frac{1}{2}(x+3)\rightarrow y=\frac{1}{2}x+3\rightarrow y-\frac{1}{2}x=3 \\ y-5=x-4\rightarrow y-x=-4+5\rightarrow y-x=1 \end{gathered}[/tex]