To solve this system of equations, we can use the method of substitution or elimination.
1. Method of substitution:
From the second equation, we can isolate y:
-2x + y = 8
y = 8 + 2x
Now substitute this expression for y into the first equation:
3x + 2(8 + 2x) = 2
3x + 16 + 4x = 2
7x + 16 = 2
7x = -14
x = -2
Substitute the value of x back into the second equation to find y:
-2(-2) + y = 8
4 + y = 8
y = 8 - 4
y = 4
Therefore, the solution to the system of equations is x = -2 and y = 4.
2. Method of elimination:
Multiply the second equation by 2 to make the coefficients of y match:
-4x + 2y = 16
Add the two equations together:
(3x + 2y) + (-4x + 2y) = 2 + 16
- x + 4y = 18
Now, multiply the first equation by 4:
4(3x + 2y) = 4(2)
12x + 8y = 8
Now subtract this equation from the previous equation:
(-x + 4y) - (12x + 8y) = 18 - 8
- x + 4y - 12x - 8y = 10 - 8
-13x - 4y = 2
Multiply this equation by -1:
13x + 4y = -2
Add this equation to the previous equation:
(-13x - 4y) + (13x + 4y) = 2 - 2
0 = 0
This equation is always true, which means the two equations are coincident or represent the same line. Therefore, the system of equations has infinitely many solutions.
In summary, the system of equations has infinitely many solutions.
3x+2y=2
−2x+y=8
3 answers
are you sure?
My apologies for the mistake. Let's reattempt solving the system of equations.
To solve the system of equations:
Equation 1: 3x + 2y = 2
Equation 2: -2x + y = 8
We can solve this system using either the method of substitution or elimination.
1. Method of substitution:
From Equation 2, we can isolate y:
y = 8 + 2x
Now substitute this expression for y into Equation 1:
3x + 2(8 + 2x) = 2
3x + 16 + 4x = 2
7x + 16 = 2
7x = -14
x = -2
Substitute the value of x back into Equation 2 to find y:
-2(-2) + y = 8
4 + y = 8
y = 8 - 4
y = 4
Therefore, the solution to the system of equations is x = -2 and y = 4.
Let's verify this solution by substituting it into the original equations:
For Equation 1:
3(-2) + 2(4) = 2
-6 + 8 = 2
2 = 2 (LHS = RHS)
For Equation 2:
-2(-2) + 4 = 8
4 + 4 = 8
8 = 8 (LHS = RHS)
The solution satisfies both equations, so it is indeed the correct solution.
Apologies again for the earlier confusion. The correct solution to the system of equations is x = -2 and y = 4.
To solve the system of equations:
Equation 1: 3x + 2y = 2
Equation 2: -2x + y = 8
We can solve this system using either the method of substitution or elimination.
1. Method of substitution:
From Equation 2, we can isolate y:
y = 8 + 2x
Now substitute this expression for y into Equation 1:
3x + 2(8 + 2x) = 2
3x + 16 + 4x = 2
7x + 16 = 2
7x = -14
x = -2
Substitute the value of x back into Equation 2 to find y:
-2(-2) + y = 8
4 + y = 8
y = 8 - 4
y = 4
Therefore, the solution to the system of equations is x = -2 and y = 4.
Let's verify this solution by substituting it into the original equations:
For Equation 1:
3(-2) + 2(4) = 2
-6 + 8 = 2
2 = 2 (LHS = RHS)
For Equation 2:
-2(-2) + 4 = 8
4 + 4 = 8
8 = 8 (LHS = RHS)
The solution satisfies both equations, so it is indeed the correct solution.
Apologies again for the earlier confusion. The correct solution to the system of equations is x = -2 and y = 4.