Solve using the elimination method.Show work.If system has no solution state this or infinite solution
8x+10y=-34
16x-5y=-43
Note that, because of the first equation, 16x + 20y = -68.
Substitute -68 -20y for 16x in the second equation.
-68 -20y -5y = -43
-25y = 25
y = -1
8x -10 = -34
8x = -24
x = -3
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. Let's start by multiplying both sides of the second equation by 2:
2*(16x-5y) = 2*(-43)
32x - 10y = -86
Now, we have the following system of equations:
8x + 10y = -34
32x - 10y = -86
To eliminate the variable y, we will add the two equations:
(8x + 10y) + (32x - 10y) = -34 + (-86)
40x + 0y = -120
40x = -120
x = -120 / 40
x = -3
Now that we have the value of x, we can substitute it back into one of the original equations. Let's use the first equation:
8x + 10y = -34
8*(-3) + 10y = -34
-24 + 10y = -34
10y = -34 + 24
10y = -10
y = -10 / 10
y = -1
Therefore, the solution to the system of equations is x = -3 and y = -1.
There is no mention of whether the system has a unique solution, no solution, or infinitely many solutions. Since we have values for x and y that satisfy both equations, the system has a unique solution.
To solve this system of equations using the elimination method, we need to eliminate one variable by multiplying the equations by appropriate coefficients so that when we add the two equations together, one variable will cancel out.
Let's start by multiplying the first equation by 2 to eliminate x:
2(8x + 10y) = 2(-34)
16x + 20y = -68
Now, our system of equations is:
16x + 20y = -68
16x - 5y = -43
Next, we can subtract the second equation from the first equation to eliminate x:
(16x + 20y) - (16x - 5y) = -68 - (-43)
16x + 20y - 16x + 5y = -68 + 43
25y = -25
y = -25/25
y = -1
Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
8x + 10(-1) = -34
8x - 10 = -34
8x = -34 + 10
8x = -24
x = -24/8
x = -3
Therefore, the solution to the system of equations is x = -3 and y = -1.
Since we obtained unique values for both x and y, this means that the system has a unique solution.