Download Study Guide Algebra I Chapter 7 Systems of Equations, pages 374

Study Guide Algebra I
Chapter 7 Systems of Equations, pages 374 - 393
As always review your notes and homework.
REMEMBER: Solving a system can have 1 of 3 outcomes:
1.
A solution (x,y)
when the 2 lines intersect
2.
No solution
when the 2 lines are parallel
3.
Infinite solutions
when the lines are the same
1. Be able to solve systems of equations by graphing both lines and
finding the point of intersection
Examples:
Solve these equations by graphing
y = 2x – 7 & y = -x + 2
y = 2x – 7
m (slope) =
y = -x + 2
2
1
−1
m (slope) =
1
€
b (y-intercept) = -7
b (y-intercept) = 2
Graph both lines:
€
6
4
2
-10
-5
5
10
-2
-4
-6
-8
Where the 2 lines intersect is your solution  (3, -1)
2. Be able to solve systems of equations by substitution
Example: Solve these 2 equations by substitution
2x – y = 6
x + y = -12
1. Solve 1 of the equations for x or y. In this case it is easier to solve
the 2nd equation:
x + y = -12
-x
-x
subtract x from both sides
y = -x - 12
2. substitute –x - 12 into the 1st equation for y:
2x –(-x - 12) = 6
2x + x + 12 = 6
3x + 12 = 6
- 12 -12
3x = -6
3
3
x = -2
distribute the – sign
combine the x terms
solve for x
3. substitute -2 back into the 1st equation to find y
y = -x – 12
y = -(-2) – 12
y = 2 – 12 = -10
4. your answer is (-2, -10)
***WRITE YOUR ANSWER AS AN ORDERED PAIR***
3. Be able to solve linear equations by elimination.
Example: solve these equations by elimination:
7x – 8y = 6
4x + y = 9 if you multiply this equation by 8 then
the y terms will be opposite and will cancel out
8(4x + y = 9) 
32x +8y = 72
multiply ENTIRE equation by 8
Now add the 2 equations together:
32x +8y = 72
1st equation multiplied by 8
+ 7x – 8y = 6
copy 2nd equation
39x
= 78
ADD
39
39
divide by 39
x=2
solve
Once you have a value for x substitute it in either of the
ORIGINAL equations and determine the value of y:
4x + y = 9
4(2) + y = 9
substitute 2 for x
8 +y=9
y=1
solve for y
(2,1) YOUR ANSWER
***WRITE YOUR ANSWER AS AN ORDERED PAIR***
Example: Solve these equations by elimination:
3x + y = 5
6x + 2y = 10
-2(3x + y = 5)
make the y terms opposite by
multiplying the 1st equation by -2
-6x - 2y = -10 multiply ENTIRE eq by -2
+ 6x + 2y = 10 copy 2nd equation
0 = 0
ADD
since 0 = 0 this means the 2 equations are the same line so
your answer is SAME LINE or Infinite solutions

Example: solve these equations by elimination:
3x - y = -2
-9x + 3y = 3
3(3x - y = -2)
make the x terms opposite by
multiplying the 1st equation by 3

9x – 3y = -6
+ -9x + 3y = 3
0
= -3
multiply ENTIRE eq by 3
copy 2nd equation and ADD
since 0 cannot = -3 your answer is NO SOLUTION
REMEMBER you can work with EITHER the x or y terms it is your
choice.
WATCH YOUR NEGATIVE SIGNS !!!!!!!!!
REMEMBER you can multiply BOTH equations by numbers to make
opposite terms.
Example:
6x + 5y = -8
2x - 7y = 32
multiply eq. 1 by 7
multiply eq. 2 by 5
7(6x + 5y = -8) 
5(2x - 7y = 32) 
42x + 35y = -56
10x – 35y = 160
52x
= 104
x=2
6x + 5y = -8
6(2) + 5y = -8
12 + 5y = -8
5y = -20
y = -4
(2, -4) your answer
ADD
OR
6x + 5y = -8
2x - 7y = 32
-3(2x - 7y = 32)
multiply eq 2 by -3

6x + 5y = -8
-6x +21y = -96
26y = -104
y = -4
ADD
2x - 7y = 32
2x -7(-4) = 32
2x + 28 = 32
2x = 4
x=2
(2, -4) your answer
4. Be able to solve word problems using systems of equations
To receive full credit you must show all work and have 3 elements in
your solution:
1. A let statement
2. 2 equations
3. Your answer must be in a sentence
For examples look at notes and homework.