Question 480673: Please answer problem 1 graphically with complete solutions and checking:
# 1) x + y = 5
x - y = -3
Please answer problem 2 by substitution method with complete solutions and checking:
# 2) x = 3y + 4
2x – 8y – 6 = 0
Please answer problem 3 by elimination method with complete solutions and checking:
# 3) 2x + 5y = - 8
3x – y = 5
Would appreciate if you can solve it step by step for me to understand it better. Thanks in advance.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Please answer problem 1 graphically with complete solutions and checking:
# 1) x + y = 5
x - y = -3
put both equations into the slope/intercept form: y = mx + 2
y = -x + 5
and
-y = -x - 3
y has to be positive, multiply both sides by -1
y = x + 3
:
We will plot two coordinates for each each equation, x=2 and x=-2,
y = -x + 5, (Red)
x | y
-------
2 | 3, y = -(2) + 5
-2 | 7, y = -(-2) + 5
and
y = x + 3, (Green)
x | y
-------
2 | 5; y = 2 + 3
-2 | 3; y = -2 + 3
:
Plot the two on the same graph, should look like this:
you can see that the point of intersection: x=1, y=4, is the solution
Check this by putting 1 for x and 4 for y in both original equations
:
:
Please answer problem 2 by substitution method with complete solutions and checking:
# 2) x = 3y + 4
2x – 8y – 6 = 0
we will use the 1st equation for substitution just like it is but
will write the 2nd equation in the standard form
2x - 8y = +6
Substitute (3y+4) x in the above equation
2(3y+4) - 8y = 6
6y + 8 - 8y = 6
6y - 8y = 6 - 8
-2y = -2
y has to be positive, multiply both sides by -1
2y = 2
y = 2/2
y = 1
Find x using the 1st equation
x = 3(1) + 4
x = 7
The solution x=7, y=1
You can check these solutions in the 2nd original equation
:
:
Please answer problem 3 by elimination method with complete solutions and checking:
2x + 5y = -8
3x – y = 5
Multiply the 2nd equation by 5, add to the 1st equation
2x + 5y = -8
15x -5y = 25
------------------addition will eliminate y, find x
17x = 17
x = 17/17
x = 1
Find y using the 1st equation 2x + 5y = -8
2(1) + 5y = -8
5y = - 8 - 2
5y = -10
y = -10/5
y = -2
The solution: x=1, y=-2
You can check these solutions in both original equations
:
Did you understand this, any questions?
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