1. Explain, in complete sentences, how you would use the graphing method to solve the following system of equations and what the final solution will look like on the coordinate plane.
x + y _<_ -5
4x - 5y > -15
2. Use the substitution method to solve the following system of equations.
6x + 3y = -7
12x + y = 6
A.) 5/6, -4
B.) -5/6, 4
C.) 5/6, 4
D.) -5/6, -4
MY ANSWER IS B
3. If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable y is eliminated in the first and second equations, then the second and third equations.
3x - y + 3z = 1
4x + y - 6z = 3
4x - 2y + 3z = -3 (4 points)
Answer options:
A.) 7x - 3z = 4
12x - 9z = 3
B.) 7x - 3z = 4
4x - 6z = 3
C.) 3x + 3z = 1
12x - 9z = 3
D.) 3x + 3z = 1
4x - 6z = 3
MY ANSWER IS C
4. Explain, in complete sentences, which method you would use to solve the following system of equations and why you chose that method. Provide the solution to the system.
x - 3y + 2z = -12
x + 2y + 3z = 6
2x - 3y - z = -2 (4 points)
5. Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. Provide the solution to the system.
5x - 3y = 1
7x - 4y = 2 (4 points)
x + y _<_ -5
4x - 5y > -15
2. Use the substitution method to solve the following system of equations.
6x + 3y = -7
12x + y = 6
A.) 5/6, -4
B.) -5/6, 4
C.) 5/6, 4
D.) -5/6, -4
MY ANSWER IS B
3. If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable y is eliminated in the first and second equations, then the second and third equations.
3x - y + 3z = 1
4x + y - 6z = 3
4x - 2y + 3z = -3 (4 points)
Answer options:
A.) 7x - 3z = 4
12x - 9z = 3
B.) 7x - 3z = 4
4x - 6z = 3
C.) 3x + 3z = 1
12x - 9z = 3
D.) 3x + 3z = 1
4x - 6z = 3
MY ANSWER IS C
4. Explain, in complete sentences, which method you would use to solve the following system of equations and why you chose that method. Provide the solution to the system.
x - 3y + 2z = -12
x + 2y + 3z = 6
2x - 3y - z = -2 (4 points)
5. Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. Provide the solution to the system.
5x - 3y = 1
7x - 4y = 2 (4 points)
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2) Standard form: 6x+3y=-7; 12x+y=6;
substitute/eliminate x = -1/2y-7/6
substitute/eliminate y = -4
Solution: x = 5/6; y = -4;
(x, y) = (0.8333, -4)
3) Standard form: 3x-y+3z=1; 4x+y-6z=3; 4x-2y+3z=-3;
substitute/eliminate x = +1/3y-1z+1/3
substitute/eliminate y = +30/7z+5/7
substitute/eliminate z = +0y+1
Solution: x = 1; y = 5; z = 1;
(x, y, z) = (1, 5, 1)
4) Standard form: x-3y+2z=-12; x+2y+3z=6; 2x-3y-z=-2;
substitute/eliminate x = +3y-2z-12
substitute/eliminate y = -1/5z+18/5
substitute/eliminate z = -2
Solution: x = 4; y = 4; z = -2;
(x, y, z) = (4, 4, -2)
5) Standard form: 5x-3y=1; 7x-4y=2;
substitute/eliminate x = +3/5y+1/5
substitute/eliminate y = +3
Solution: x = 2; y = 3;
(x, y) = (2, 3)
substitute/eliminate x = -1/2y-7/6
substitute/eliminate y = -4
Solution: x = 5/6; y = -4;
(x, y) = (0.8333, -4)
3) Standard form: 3x-y+3z=1; 4x+y-6z=3; 4x-2y+3z=-3;
substitute/eliminate x = +1/3y-1z+1/3
substitute/eliminate y = +30/7z+5/7
substitute/eliminate z = +0y+1
Solution: x = 1; y = 5; z = 1;
(x, y, z) = (1, 5, 1)
4) Standard form: x-3y+2z=-12; x+2y+3z=6; 2x-3y-z=-2;
substitute/eliminate x = +3y-2z-12
substitute/eliminate y = -1/5z+18/5
substitute/eliminate z = -2
Solution: x = 4; y = 4; z = -2;
(x, y, z) = (4, 4, -2)
5) Standard form: 5x-3y=1; 7x-4y=2;
substitute/eliminate x = +3/5y+1/5
substitute/eliminate y = +3
Solution: x = 2; y = 3;
(x, y) = (2, 3)