Question

what is the solution to the system of equation graphed below?*write your answer as an ordered pair*

Answer 1

Solve by graph

the solution of two lines is the point where they bisect

then , solution point is

$(4,5)$

Solve by functions

we write the equation of each line, general equation of a line is

$y=mx+b$

where m is the slope and b the y-intercept

we find the slope using the formula and two points

$m=\frac{y2-y1}{x2-x1}$

where (x2,y2) is a right point from (x1,y1)

green line

find the slope with points (0,1) and (1,2)

$\begin{gathered} m=\frac{2-1}{1-0} \\ \\ m=1 \end{gathered}$

and y-intercept is 1, then b=1

the equation of the green line is

$y=x+1$

yellow line

find the slope with points (-2,2) and (0,3)

$\begin{gathered} m=\frac{3-2}{0-(-2)} \\ \\ m=\frac{1}{2} \end{gathered}$

and y-intercept is 3 then b=3

the equation of the yellow line is

$y=\frac{1}{2}x+3$

now we have two equations

$\begin{gathered} y=x+1 \\ y=\frac{1}{2}x+3 \end{gathered}$

we replace the value of y of any equation on the other equation

i will repalce y from the first equation on the second

$x+1=\frac{1}{2}x+3$

and solve for x

$\begin{gathered} x-\frac{1}{2}x=3-1 \\ \\ (1-\frac{1}{2})x=2 \\ \\ \frac{1}{2}x=2 \\ \\ x=2\times2=4 \end{gathered}$

the value of x is 4, now i can repalce x=4 on any equation to find y

i will replace x on the first equation

$\begin{gathered} y=4+1 \\ y=5 \end{gathered}$

the value of y is 5

the point solution is

$(4,5)$