Download Solving Systems of Equations, Part 1 1. Solve the following system

Solving Systems of Equations, Part 1
1. Solve the following system of equations by graphing:
2x + y = 1, 3x + y = 0
4
3
2
1
-5
-4
-3
-2
0
-1 -1 0
1
2
3
4
5
-2
-3
-4
(-1, 3)
2. Solve the following system of equations by graphing:
y = 3, x = 3y + 6
(15,3)
3. Solve the following system of equations by graphing:
2x + y = 1, 3x + y = 0
(-1, 3)
Solve the following systems of equations by Substitution:
4. 3x + y = -14, 4x + 3y = -22
y = -3x – 14 subst into 2nd: 4x + 3(-3x – 14) = -22, 4x - 9x - 42 = -22, -5x = 20, x = -4
3(-4) + y = -14, y = -2
check (-4, -2): 3(-4) + -2 = -14, OK; 4(-4) + 3(-2) = -16-6 = -22 OK
5. 2y = x+2, 6x -12y = 0
Divide the 2nd by 6 giving x – 2y = 0. Note that the slopes are the same and intercepts different
No solution
6. ¼ x – 2y = 1, x – 8y = 4
Multiply 1st by 4: x – 8y = 4; They are the same equation: Infinite solutions.
7. 5x + 2y – 4x – 2y = 2(2y + 6) – 7, 3(2x – y) – 4x = 1 + 9
x = 4y + 12 – 7 = 4y + 5, x = 4y + 5 is first
6x – 3y – 4x = 10 or 2x – 3y = 10 is second
subst x from 1st into 2nd: 2(4y + 5) -3y = 10, 8y – 3y + 10 = 10, y = 0
from 1st: x = 4(0) + 5=5, x = 5
Check: (5) = 4(0) + 5, OK, 2(5) – 3(0) = 10 OK
8. 2x + 4y = 6, 5x + 10y = 16
1st becomes, after divide by 2: x + 2y = 3, second, after divide by 5, x + 2y = 16/5
same slope, different intercept, no solution