-7x+7y=7 2x-2=-18 how many solutions does this system have ?
To determine the number of solutions for the given system of equations, we need to solve the equations simultaneously. Let's solve them step-by-step:
1. Start with the first equation: -7x + 7y = 7.
First, let's isolate one variable. We can isolate x by subtracting 7y from both sides of the equation:
-7x = -7y + 7.
2. Divide both sides of the equation by -7 to solve for x:
x = (7y - 7) / -7.
3. Simplify the expression:
x = -y + 1.
Now, let's move on to the second equation: 2x - 2 = -18.
4. Add 2 to both sides of the equation to isolate the term with x:
2x = -18 + 2.
5. Simplify the expression:
2x = -16.
6. Divide both sides of the equation by 2 to solve for x:
x = -16 / 2.
7. Simplify the expression:
x = -8.
Now we have the values of x in terms of y from the first equation (x = -y + 1) and a specific value for x from the second equation (x = -8).
8. Substitute the value of x from the second equation (-8) into the first equation:
-8 = -y + 1.
9. Add y to both sides of the equation to isolate y:
y - 8 = 1.
10. Add 8 to both sides of the equation:
y = 1 + 8.
11. Simplify the expression:
y = 9.
Now we have the values of x (-8) and y (9) that satisfy both equations.
Since we have found a specific solution for x and y, the system of equations has a single unique solution. Therefore, the system has only one solution.
To find the number of solutions for the given system of equations, we can solve the equations simultaneously. Let's begin.
1) -7x + 7y = 7
We can rearrange this equation to solve for x:
-7x = -7y + 7
x = (7y - 7)/(-7)
x = y - 1
2) 2x - 2 = -18
Again, we rearrange this equation to solve for x:
2x = -18 + 2
2x = -16
x = -16/2
x = -8
Now, we have the value of x in terms of y from equation 1, and the actual value of x from equation 2. By comparing these values, we can determine the number of solutions:
x = y - 1 and x = -8
If we equate these two expressions:
y - 1 = -8
y = -8 + 1
y = -7
So, the system has one unique solution, where x = -8 and y = -7.
2x-2= -18
2x= -18+2= -16 Divide with 2
x=-8
-7x+7y=7
-7*(-8)+7y=7
56+7y=7
7y=7-56
7y= -49 Divide with 7
y= -7
One solution x= -8 y= -7