Question

unit 4b solving systems of equations using graphs
mild\tmedium\tspicy
student can use a graph of two equations to find the solution for a system of equations.\tstudent can create graphs to find the solution for a system of equations.\tstudent can create graphs to find the solution for a system of equations and then use substitution to prove that solution.
the graphs of $y = -\frac{3}{4}x + 1$ and $y = \frac{1}{4}x - 3$ are shown below. what is the solution to this system of equations?
find the solution to the following system of equations by graphing.
$y = -\frac{3}{5}x - 1$
$y = -x - 3$
use substitution to prove that your answer to the previous problem is correct. if it is not, go back and identify your error(s).

Explanation:

Step1: Solve first system

Set $-\frac{3}{4}x + 1 = \frac{1}{4}x - 3$. Combine terms: $1 + 3 = \frac{1}{4}x + \frac{3}{4}x \Rightarrow 4 = x$. Substitute $x=4$ into $y=-\frac{3}{4}(4)+1=-2$. Solution: (4,-2)

Step2: Solve second system

Set $-\frac{3}{5}x -1 = -x -3$. Combine terms: $-1 + 3 = -x + \frac{3}{5}x \Rightarrow 2 = -\frac{2}{5}x \Rightarrow x=-5$. Substitute $x=-5$ into $y=-(-5)-3=2$. Solution: (-5,2)

Answer:

(4, -2), (-5, 2)