Hello. I am having a bit of trouble understanding the following
"Solve by Graphing.
3x + y = 5
-2x + 3y = 4"
I know you can't see the graphing on this site, but I would really appreciate it if someone points me in the right direction in how to do this.
put both equations in slope intercept form:
y= -3x+5
y=2/3 x+4/3
check those.
Now graph each. What is each y when x is zero?
what is y when x is 3?
draw lines representing each equation. THe solution is the common point, where they intersect.
Thanks! This helped alot.
Of course! I'll explain how to solve the system of equations by graphing.
To solve the system of equations graphically, you need to plot the lines represented by each equation on a coordinate plane and find the point where the lines intersect. This point represents the solution to the system.
Let's start with the first equation, 3x + y = 5. To graph this equation, you need to rearrange it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we get y = -3x + 5. Now we can easily determine the slope, which is -3, and the y-intercept, which is 5.
Plot the y-intercept by placing a point at (0, 5). Then, use the slope to find another point on the line. The slope of -3 means that for every one unit increase in x, y will decrease by three units. So, starting from the y-intercept (0, 5), move to the right one unit (increase x by 1) and down three units (decrease y by 3). Plot another point at this new position.
Now, draw a straight line through the two plotted points. This line represents the first equation.
Next, let's move on to the second equation, -2x + 3y = 4. Again, rearrange it into slope-intercept form:
3y = 2x + 4
y = (2/3)x + 4/3
The slope is 2/3 and the y-intercept is 4/3. Plot the y-intercept at (0, 4/3) and find another point using the slope. Starting at the y-intercept, move to the right three units (increase x by 3) and up two units (increase y by 2). Plot another point at this new position.
Draw a straight line through the two points, and this line represents the second equation.
Now, analyze the graph and see where the two lines intersect. The point of intersection represents the solution to the system of equations. In this case, if the lines intersect at a single point, it means there is one unique solution. If the lines are parallel and do not intersect, it means there is no solution. If the lines coincide (overlap), it means there are infinite solutions.
By examining the graph and finding the point of intersection, you can determine the solution to this system of equations.