Systems by graphing: look at example on page 276 and summary on p.278
Systems by Substitution: look at p.282, 283
y = 3x – 5
y = 2x + 2
plug in: 3x – 5 = 2x + 2
-2x
-2x
x–5= 2
+5 +5
x = 7 plug in x to find y
answer: (7, 16)
OR
plug in:
2x + 3y = 10
x = 2y - 2
2(2y - 2) + 3y = 10
4y - 4 + 3y = 10
7y - 4 = 10
+4 +4
7y = 14
y=2
answer: (2, 2)
plug in y to find x
Systems by elimination: (look at example 1 & 5 on p.287 and 290)
Use addition (or subtraction) method if both equations are in the standard form:
like: 2x - y = 10
5x + y = 11
or
(add these together to eliminate the y)
3x + 2y = 12
x + 2y = 4
(subtract these to eliminate the y)
2x - y = 10
+ 5x + y = 11
7x
x
3x + 2y = 12
− ( x + 2y = 4 )
= 21
= 3
2x
x
now plug x = 3 into either of your equations
to find y
make sure you subtract all 3 terms
= 8
= 4
now plug x = 4 into either of your equations
to find y
Sometimes to use the addition or subtraction method we have to multiply 1st:
Like:
2x - y = 1
x + 3y = 4
we cannot eliminate x or y!
if we multiply the 1st equation by 3, then we can eliminate y
3(2x - y = 1)
6x - 3y = 3
+ x + 3y = 4
7x = 7
x =1
now you can add the equations to eliminate y
plug x = 1 into either of the equations to find y
Review:
31. Find the slope of the line containing: (-3, 9) and (-5, 11)
32. Add: -7 + (-3) + (-12) + 16
33. Use order of operations to solve: 2³- 7 + 16 ÷ (-3 + 5)
34. Solve: 3(2x - 5) = 8x - 9
35. Solve: 6 - 2(5x - 8) = 3x - 4
36. Solve for y: -3x + 5y = 15
37. Find the slope and y-intercept: y = 5x - 9
38. Find the slope and y-intercept: 2x + 4y = 8
39. Write the equation of the line with a y-intercept of (0, -3) and a slope of ½
40. Is (-10, 0) a solution of y = -3x -30?
Systems Review
show work
Name:
Use addition to solve for (x , y) in these system of equations:
1. 2x - y = 12
3x + y = 8
2. 3x + y = 11
7x - y = 19
5. 3x - 3y = 12
5x + 3y = 4
3. x - y = 8
x+y=4
6. 4x + 5y = 16
-4x + 2y = 5
4. -5x + y = 9
-2x - y = 5
7. -9x + 3y = 18
9x + 2y = -3
8. -5x - 3y = -10
5x - 3y = -20
Sometimes we have to multiply one of the equations 1st:
Like:
2x - y = 1 we cannot eliminate x or y!
x + 3y = 4
if we multiply the 1st equation by 3, then we can eliminate y
3(2x - y = 1)
6x - 3y = 3
+ x + 3y = 4 now you can add the equations to eliminate y
7x
= 7
x =1
plug x = 1 into either of the equations to find y
9.
x - 2y = 4
3x + 4y = 2
12. 4x + 3y = 15
2x - 5y = 1
10. 4x - 5y = 22
x + 2y = -1
11. 3x - y = 11
2x + 5y = 13
13. 5x - 2y = -1
x+y=4
14. 4x - 3y = 1
8x + 5y = 13
Review:
15. Find the slope of the line containing: (-3, 9) and (-5, 11)
16. Add: -7 + (-3) + (-12) + 16
17. Use order of operations to solve: 2³- 7 + 16 ÷ (-3 + 5)
18. Solve: 3(2x - 5) = 8x - 9
19. Solve: 6 - 2(5x - 8) = 3x - 4
20. Solve for y: -3x + 5y = 15
21. Find the slope and y-intercept: y = 5x - 9
22. Find the slope and y-intercept: 2x + 4y = 8
23. Write the equation of the line with a y-intercept of (0, -3) and a slope of ½
24. Is (-10, 0) a solution of y = -3x -30? show work