Solve the system of equations by graphing
2x+y=8
X+3y=9
y = 2, x = 3
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To solve the system of equations by graphing, you need to plot the lines represented by each equation on a coordinate plane and find the point where the lines intersect. That point of intersection is the solution to the system of equations.
Let's graph each equation one by one:
1. Start with the first equation: 2x + y = 8
To graph this equation, we need to first rewrite it in slope-intercept form (y = mx + b), where m represents the slope, and b represents the y-intercept.
Rearrange the equation to isolate y:
y = -2x + 8
Now we can graph this equation. To do so:
Step 1: Choose any x value and plug it into the equation to find the corresponding y value.
Let's choose x = 0:
y = -2(0) + 8
y = 8
So, the point (0, 8) is on the graph.
Step 2: Connect this point with at least one more point to form a line.
Let's choose x = 4:
y = -2(4) + 8
y = 0
We now have two points: (0, 8) and (4, 0). Plot these points and draw a line through them.
2. Move on to the second equation: x + 3y = 9
Rewrite the equation in slope-intercept form:
3y = -x + 9
y = (-1/3)x + 3
Again, let's graph this equation using the steps outlined above:
Step 1: Choose any x value and find the corresponding y value.
Let x = 0:
y = (-1/3)(0) + 3
y = 3
So, the point (0, 3) is on the graph.
Step 2: Choose another x value and find the corresponding y value.
Let x = 6:
y = (-1/3)(6) + 3
y = 1
We now have two points: (0, 3) and (6, 1). Plot these points and draw a line through them.
Now, look at the graphed lines. The point where they intersect is the solution to the system of equations. In this case, it looks like the lines intersect at the point (3, 2).
Therefore, the solution to the system of equations is x = 3 and y = 2.