Question 62120This question is from textbook beginning algebra
: THE INSTRUCTIONS SAYS: SOLVE THE SYSTEM OF EQUATIONS USING SUBSTITUTION METHOD
1. X=y+5
x-y+1
3. x-y+5
3x+2y+7
5. 2x-y+-5
4x+y=2
7. x+2y=9
x+2y+1
I AM VERY CONFUSED WORKING AND SOLVING THE SYSTEM OF EQUATIONS USING SUBSTITUTION METHOD.. HELP!!
This question is from textbook beginning algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! THE INSTRUCTIONS SAYS: SOLVE THE SYSTEM OF EQUATIONS USING SUBSTITUTION METHOD
Some of these problems are not equations and/or are inconsistent (no solution),
I will change them so the can be solved, and give you detailed instructions on
the substitution method.
:
Below you see that we have x = y+5; that means that wherever we have an x in the 2nd eq; (2x - y = 1), we can substitute (y+5) for x, let's do that now:
:
x = y+5; this is what we are using to substitute
:
2x - y = 1
Substitute (y+5) for x:
2(y+5) - y = 1
Mult what's inside the brackets and solve for y
2y + 10 - y = 1
Subtract 10 from both sides:
2y - y = 1 - 10
1y = - 9
or just: y = -9
;
We need to find the value of x now, substitute -9 for y in the 1st equation
x = y + 5
x = -9 + 5
x = -4
:
So the solutions are x = -4, y = -9, to be sure, let's substitute for x and y in the equation: 2x - y = 1:
2(-4) - (-9) = 1`
-8 + 9 = 1: remember minus a minus is a plus
:
:
Neither one of these are equations,
3. x-y+5
3x+2y+7
I will change them so they are:
x = y + 5
3x - 2y = 7
:
In this one x = y + 5 again, substitute for x in the 2nd equation:
3(y+5) - 2y = 7
3y + 15 - 2y = 7
3y - 2y = 7 - 15
y = -8
:
Find x, substitute -8 for y in the 1st equation, x = y + 5
x = -8 + 5
x = -3
:
Our solution is x =-3 and y = -8. Check by substitution in 3x - 2y = 7
3(-3) - 2(-8) = 7
-9 - (-16) = 7
-9 + 16 = 7, checks our solutions
:
:
:
5.
2x - y = -5
We have to rearrange so we can solve for y, y has to be positive
-y = -5 - 2x
Mult eq by -1 to get rid of the neg y, you have
y = 5 + 2x
:
Substitute (2x+5) for y in the 2nd equation:
4x + y = 2
4x + (2x+5) = 2
4x + 2x = 2 - 5
6x = -3
Divide both sides by 6:
x = -3/6
x = -(1/2)
:
Find y, substitute (-1/2) for x in the 1st equation;
y = 2(-1/2) + 5
y = -1 + 5
y = +4
;
Our solutions are x = -(1/2 and y = +4; check our solutions in the 2nd equation
4x + y = 2
4(-1/2) + 4 = 2
-2 + 4 = +2; check our solutions
:
:
:
7.
x + 2y = 9
Rearrange so we can solve for x, subtract 2y from both sides:
x = 9 - 2y,
:
Substitute (9-2y) for x in the 2nd equation:
x - 2y = 1
(9-2y) + 2y = 1
9 - 2y - 2y = 1
-4y = 1 - 9
-4y = -8
Divide both sides by -4
y = -8/-4
y = +2
:
Find x, substitute +2 for y in the 1st equation: x + 2y = 9
x + 2(2) = 9
x + 4 = 9
x = 9 - 4
x = +5
:
Our solutions: x = 5, y = 2; check by substitution in the eq: x - 2y = 1
5 - 2(2) = 1, checks our solutions
:
I suggest that you print this out and study each step until it becomes clear to you. Good luck
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