Question 68532This question is from textbook Algebra 1 for Chirstian Schools
: 2x + y = 15
x + 2y = 18
This question is from textbook Algebra 1 for Chirstian Schools
Answer by rmromero(383)   (Show Source):
You can put this solution on YOUR website! There are several Steps to Graph these equations.
One way is by Using the Slope - Intercept Form.
1. Rewrite the equation to y = mx + b, where m = the slope and b = y-intercept.
From --->2x + y = 15
y = -2x + 15 , m = -2 and b = 15
To graph the b will help you plot the first point. Since b = 15, you point is located (0, 15).The m is the  . Since m = -2, we can rewrite it  . From point (0, 15), we will move 2 units down because 2 is negative and 1 unit right because 1 is positive.
2. x + 2y = 18
Rewrite the equation to y = mx + b.
x + 2y = 18
2y = -x + 18
 , m =  b = 9 ,
From point (0, 9), we will move 1 unit down and 2 units right.
If you want to combine the two equation, the graph looks like this.
Green line is the graph of x + 2y = 18 and the red line shows the graph of 2x + y = 15
If you want to find the intersection of the graph: Here are the Steps using Substition method
1. In either equation, solve for one variable in terms of the other.
x + 2y = 18
x = -2y +18
2. Substitute -2y + 18 for x in the other equation 2x + y = 15. Solve y.
2x + y = 15
2(-2y+18) + y = 15
-4y + 36 + y = 15
-3y = -21
y = 7
3. Substitute the result from step 2 in either equation. Solve for the other variable.
2x + y = 15 , y = 7
2x + 7 = 15
2x = 8
x = 4
4. Check the solution in both original equations.
2x + y = 15 , x = 4 and y = 7
2(4) + 7 = 15
8 + 7 = 15
15 = 15 ----------->> True
x + 2y = 18, x = 4 and y = 7
4 + 2(7) = 18
4 + 14 = 18
18 = 18 ---------->> True
The Solution of the equation is x = 4 and y = 7, Meaning the graph will meet when x = 4 and y = 7
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