Solve the system by f equations -x+6y=13 4x-10y=-10
To solve the system of equations:
1) -x + 6y = 13
2) 4x - 10y = -10
We can solve it using the substitution method or the elimination method. Let's use the elimination method to solve it.
To eliminate x, let's multiply equation 1 by 4 and equation 2 by -1:
1) -4x + 24y = 52
2) -4x + 10y = 10
Now subtract equation 2 from equation 1:
(-4x + 24y) - (-4x + 10y) = 52 - 10
Simplifying:
-4x + 24y + 4x - 10y = 42y = 42
Dividing both sides by 42:
y = 1
Now substitute this value for y back into equation 1 or equation 2:
-x + 6(1) = 13
-x + 6 = 13
-x = 13 - 6
-x = 7
x = -7
So the solution to the system of equations is x = -7 and y = 1.
To solve the given system of equations:
Equation 1: -x + 6y = 13
Equation 2: 4x - 10y = -10
Step 1: Solve Equation 1 for x:
-x = 13 - 6y
Multiplying both sides by -1 to get x alone:
x = -13 + 6y
Step 2: Substitute the value of x in Equation 2:
4(-13 + 6y) - 10y = -10
Expanding and simplifying:
-52 + 24y - 10y = -10
Combine like terms:
14y - 52 = -10
Step 3: Solve Equation 3 for y:
14y = -10 + 52
14y = 42
Divide both sides by 14:
y = 3
Step 4: Substitute the value of y into Equation 1 or Equation 2 to solve for x. Let's substitute it into Equation 1:
x = -13 + 6(3)
x = -13 + 18
x = 5
Solution:
The solution to the system of equations is x = 5 and y = 3.
To solve the given system of equations:
1. We have the first equation: -x + 6y = 13.
We can rearrange it to isolate x: x = 6y - 13.
2. Now let's move on to the second equation: 4x - 10y = -10.
Substitute the value of x from the first equation into the second equation:
4(6y - 13) - 10y = -10.
3. Simplify and solve the equation:
24y - 52 - 10y = -10.
Combine like terms: 14y - 52 = -10.
Add 52 to both sides: 14y = 42.
Divide both sides by 14: y = 3.
4. Now substitute the value of y back into the first equation to find x:
x = 6(3) - 13.
Simplify: x = 18 - 13.
Calculate: x = 5.
Therefore, the solution to the given system of equations is x=5 and y=3.