SOLUTION: Can you please solve the following by graphing. Demonstrate on the graph what the solution means. Then solve algebraically by substitution and then again by the addition property

Question 515347: Can you please solve the following by graphing. Demonstrate on the graph what the solution means. Then solve algebraically by substitution and then
again by the addition property of equality?
2x + y = 6
y - x = -3
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
First, you have to recognize that you have linear equations.
The addition and subtraction property of equality is that:
if a = b, then a+c = b+c, and a-c = b-c.
You often use this property in solving problems.
.
2x + y = 6
y -x = -3
.
rearranged...
.
2x + y = 6
-x +y = -3
.
subtract the 2nd equation from the 1st and you get:
.
3x = 9
x = 3
.
substitute x=3 to find y
.
2x + y = 6
2(3) + y = 6
6 + y = 6
y = 0
.
So, the lines intersect at: (3,0)
.
Or you could have solved by elimination.
.
Gien y-x =-3
y -x+x = -3+x (the addition property)
.
y = -3+3 = 0
.
substitute y=0 to find x
.
2x +y = 6
2x +0 = 6
2x = 6
x = 3
.
Again, this tells us the lines intersect at (3,0).
Another way of saying this is that the point (3,0) satisfies both equations.
.
To graph it is easiest to use the slope-intercept form:
2x + y = 6
y -x = -3
.
which become
y = -2x +6
y = x-3
.
In this graph the first equation is red and the second is green.
.

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