What is the graph of the system y = −2x + 3 and 2x + 4y = −8?

Question

mathmale · Answer

You'll need to draw this system.  Check out the Draw utility, below.  You can ask for help with this utility if need be.

whpalmer4 · Answer

these are linear equations, and when you graph them, you get straight lines.   We can see that they are linear because there are no exponents on the variables.

Graphing linear equations is very easy.  Here is one quick approach.  

set $x=0$ and find value of $y$. Make a mark on the graph at $(0,y)$.
set $y=0$ and find the value of $x$. Make a mark on the graph at $(x,0)$.
draw a straight line through the two points you marked.

for your first equation, $$y=-2x+3$$
$$y=-2(0)+3=3$$mark point at $(0,3)$
$$0=-2x+3$$$$0+2x=-2x+3+2$$$$2x=3$$$$\frac{2x}2=\frac{3}2$$$$x=\frac{3}2$$mark second point at $(3/2,0)$ and draw line

repeat process with other equation.  

If all of the lines intersect in a point, that point is the solution to the system of equations, a set of values which makes all of them true number sentences.  Sometimes you have parallel lines, which means there are no solutions.  At other times, you end up with lines which are identical, and that means that every point on the line is a solution, giving you infinitely many solutions. Be glad you don't have to list each one 😀