Chapter 2: Equations and Inequalities 2.2: Solving Equations Algebraically
CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.
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Transcript of CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.
![Page 1: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/1.jpg)
CHAPTER 7
REVIE
W
SO
LVI N
G S
YS
TE
MS
OF E
QU
AT
I ON
S A
ND
I NE
QU
AL I T
I ES
![Page 2: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/2.jpg)
1. WHAT WOULD BE THE EASIEST METHOD TO SOLVE THIS SYSTEM? WHY?
Now solve it
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2. WHAT WOULD BE THE EASIEST METHOD TO SOLVE THIS SYSTEM? WHY?
Now solve it
![Page 4: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/4.jpg)
3. WHAT WOULD BE THE EASIEST METHOD TO SOLVE THIS SYSTEM? WHY?
Now solve it
![Page 5: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/5.jpg)
4. AMANDA HAS 37 COINS IN QUARTERS AND DIMES TOTALING $6.55.
HOW MANY OF EACH DOES SHE HAVE?
WRITE A SYSTEM OF EQUATIONS AND SOLVE.
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5. JOE’S PRIVATE JET FLIES TO HAWAII AT A RATE OF 555 MPH WITH THE WIND, ON THE WAY
HOME HE FLIES 475 MPH AGAINST THE WIND. WRITE AND SOLVE A SYSTEM OF EQUATIONS TO FIND THE SPEED OF THE JET
IN STILL AIR, AND THE WIND SPEED.
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6. SODA A HAS 12% SUGAR PER OUNCE AND SODA B HAS 17% SUGAR PER OUNCE. DANIEL MIXES THE TWO SODAS TO CREATE A 32 OZ. SODA MIX WITH 15% SUGAR PER OUNCE. HOW MUCH OF EACH SODA DID HE USE?
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7. GRAPH THE INEQUALITY
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8. GRAPH THE INEQUALITY
![Page 10: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/10.jpg)
9. Write the system of inequalities represented by the graph.
![Page 11: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/11.jpg)
10. Write the system of inequalities represented by the graph.
![Page 12: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/12.jpg)
11. Write the system of inequalities represented by the graph.
![Page 13: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/13.jpg)
12. GRAPH THE SYSTEM OF INEQUALITIES.
![Page 14: CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1a5503460f94c2fc4c/html5/thumbnails/14.jpg)
13. SOLVE THE FOLLOWING SYSTEM OF EQUATIONS.
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THE SOLUTIONS START ON THE NEXT
PAGE.
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1. SUBSTITUTION IS PROBABLY EASIEST.
THEREFORE
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2. SUBSTITUTION IS PROBABLY EASIEST.
THEREFORE
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3. SUBSTITUTION OR GRAPHING WOULD BE EASIEST.
SINCE THE TWO LINES HAVE THE SAME SLOPE AND DIFFERENT Y-INTERCEPTS, THEY ARE PARALLEL. THEREFORE THERE IS NO SOLUTION.OR
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4. AMANDA HAS 37 COINS IN QUARTERS AND DIMES TOTALING $6.55:
I WOULD DIVIDE THE BOTTOM EQUATION BY 5, AND MULTIPLY THE TOP EQUATION BY 2 TO GET:
SUBTRACTING YIELDS:
THEREFORE SHE HAS 18 DIMES AND 19 QUARTERS
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5. JOE’S PRIVATE JET FLIES TO HAWAII AT A RATE OF 555 MPH WITH THE WIND, ON THE WAY HOME HE FLIES 475 MPH AGAINST THE WIND.
ADDING THE EQUATIONS TOGETHER YIELDS:
SO THE JET IS GOING 515 MPH AND THE WIND IS BLOWING AT40 MPH
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6. SODA A HAS 12% SUGAR PER OUNCE AND SODA B HAS 17% SUGAR PER OUNCE. DANIEL MIXES THE TWO SODAS TO CREATE A 32 OZ. SODA MIX WITH 15% SUGAR PER OUNCE.
MULTIPLYING THE TOP EQUATION BY 12 AND THE BOTTOM EQUATION BY 100 YIELDS:
STHEREFORE, DANIEL USED 19.2 OZ. OF A AND 12.8 OZ. OF B.
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7.
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8.
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9.
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10.
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11.
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12.
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13.
SUBTRACTING THE LAST EQUATION FROM THE FIRST YIELDS:
SO SUBSTITUTING THAT INTO THE FIRST AND SECOND EQUATIONS YIELDS A SYSTEM OF 2 EQUATIONS AND 2 UNKNOWNS:
SIMPLIFYING AND PUTTING EACH IN STANDARD FORM:
ADDING THE 2 EQUATIONS YIELDS:
SO AND . USING THIS WE CAN SOLVE FOR IN ANY OF THE EQUATIONS; WHICH GIVES US