Solving system of linear equations by using the apropiate method name the method and the x,y coordinates
1)X=4y+8
2x-8y=-3
2)3x-7y=6 elimination method
2x+7y=4 (2,0)
3)5x-2y=12 elimination method
3x-2y=-2 (7,23/2)
4)9x-8y=42 elimination method
4x+8y=-16 (2,-3)
5)X=4y+8 substitution method
2x-8y=-3 (3,1)
#2 elimination
3x-7y=6
+2x+7y=4
________
5x =10
x =2
if x is 2, you plug it in
2(2)+7y=4
7y=4-4
y=0
(2,0)
Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
4x + 4y = -36
4x + 4y = 12
X=4y+8
x-4y=-3
2x+8y=-9
To solve the system of linear equations using the appropriate method, we will consider each case separately:
1) Method: Substitution
Equation 1: X = 4y + 8
Equation 2: 2x - 8y = -3
To solve using the substitution method, we can substitute the value of X from Equation 1 into Equation 2:
2(4y + 8) - 8y = -3
8y + 16 - 8y = -3
16 = -3
Upon solving, we find that the equations are inconsistent and do not intersect at any point. Thus, there are no x, y coordinates that satisfy both equations.
2) Method: Elimination
Equation 1: 3x - 7y = 6
Equation 2: 2x + 7y = 4
To solve using the elimination method, we can add the two equations together:
(3x - 7y) + (2x + 7y) = 6 + 4
5x = 10
x = 2
Substituting the value of x back into either equation, let's use Equation 2:
2(2) + 7y = 4
4 + 7y = 4
7y = 0
y = 0
Therefore, the x, y coordinates that satisfy both equations are (2, 0).
3) Method: Elimination
Equation 1: 5x - 2y = 12
Equation 2: 3x - 2y = -2
To solve using the elimination method, we can subtract the two equations:
(5x - 2y) - (3x - 2y) = 12 - (-2)
2x = 14
x = 7
Substituting the value of x back into either equation, let's use Equation 1:
5(7) - 2y = 12
35 - 2y = 12
-2y = 12 - 35
-2y = -23
y = -23/2
Therefore, the x, y coordinates that satisfy both equations are (7, -23/2).
4) Method: Elimination
Equation 1: 9x - 8y = 42
Equation 2: 4x + 8y = -16
To solve using the elimination method, we can add the two equations together:
(9x - 8y) + (4x + 8y) = 42 - 16
13x = 26
x = 2
Substituting the value of x back into either equation, let's use Equation 1:
9(2) - 8y = 42
18 - 8y = 42
-8y = 42 - 18
-8y = 24
y = -3
Therefore, the x, y coordinates that satisfy both equations are (2, -3).
5) Method: Substitution
Equation 1: X = 4y + 8
Equation 2: 2x - 8y = -3
To solve using the substitution method, we can substitute the value of X from Equation 1 into Equation 2:
2(4y + 8) - 8y = -3
8y + 16 - 8y = -3
16 = -3
Upon solving, we find that the equations are inconsistent and do not intersect at any point. Thus, there are no x, y coordinates that satisfy both equations.
I hope this helps! Let me know if you have any other questions.