chapter 7 review solving systems of equations and inequalities

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

1. WHAT WOULD BE THE EASIEST METHOD TO SOLVE THIS SYSTEM? WHY?

Now solve it

2. WHAT WOULD BE THE EASIEST METHOD TO SOLVE THIS SYSTEM? WHY?

Now solve it

3. WHAT WOULD BE THE EASIEST METHOD TO SOLVE THIS SYSTEM? WHY?

Now solve it

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.

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.

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?

7. GRAPH THE INEQUALITY

8. GRAPH THE INEQUALITY

9. Write the system of inequalities represented by the graph.

10. Write the system of inequalities represented by the graph.

11. Write the system of inequalities represented by the graph.

12. GRAPH THE SYSTEM OF INEQUALITIES.

13. SOLVE THE FOLLOWING SYSTEM OF EQUATIONS.

THE SOLUTIONS START ON THE NEXT

PAGE.

1. SUBSTITUTION IS PROBABLY EASIEST.

THEREFORE

2. SUBSTITUTION IS PROBABLY EASIEST.

THEREFORE

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

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

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

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.

7.

8.

9.

10.

11.

12.

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