Solve the system of equations. –x%2B6y%3D13 4x–10y%3D–10 (1 point) (%2C )
give me goo answr
To solve the system of equations:
1) -x + 6y = 13 ----(1)
2) 4x - 10y = -10 ----(2)
We can solve this system using the method of substitution or elimination.
Let's solve it using the method of substitution:
From equation (1), we can write:
-x = -13 + 6y
x = 13 - 6y
Substituting this value of x in equation (2), we get:
4(13 - 6y) - 10y = -10
52 - 24y - 10y = -10
52 - 34y = -10
-34y = -10 - 52
-34y = -62
y = -62 / -34
y = 31/17
Now, substitute this value of y back in equation (1):
-x + 6(31/17) = 13
-x + 186/17 = 13
-x = 13 - 186/17
-x = (221 - 186)/17
-x = 35/17
x = -35/17
Therefore, the solution to the system of equations is:
(x, y) = (-35/17, 31/17)
To solve the system of equations:
1. Rearrange the first equation to solve for x:
-x + 6y = 13
-x = 13 - 6y
x = -13 + 6y
2. Substitute this value of x into the second equation:
4x - 10y = -10
4(-13 + 6y) - 10y = -10
3. Simplify the equation:
-52 + 24y - 10y = -10
14y = 42
y = 42 / 14
y = 3
4. Substitute the value of y back into the first equation to find x:
x = -13 + 6(3)
x = -13 + 18
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 3.
To solve the system of equations:
Equation 1: -x/2 + 6y = 13
Equation 2: 4x - 10y = -10
We can proceed using the method of substitution or elimination. Let's solve the system by elimination:
1. Multiply Equation 1 by 4 to make the coefficients of x in both equations the same:
-4x + 24y = 52
2. Subtract Equation 2 from the modified Equation 1:
(-4x + 24y) - (4x - 10y) = 52 - (-10)
-4x + 24y - 4x + 10y = 52 + 10
-8x + 34y = 62
3. Divide the equation by 2 to simplify:
-4x/2 + 34y/2 = 62/2
-2x + 17y = 31
Now we have a simpler system of equations:
Equation 1: -2x + 17y = 31
Equation 2: 4x - 10y = -10
We will solve this new system using elimination:
4. Multiply Equation 1 by 2 to eliminate the x variable:
(-2x + 17y) × 2 = 31 × 2
-4x + 34y = 62
5. Add Equation 2 to the modified Equation 1:
(-4x + 34y) + (4x - 10y) = 62 + (-10)
-4x + 34y + 4x - 10y = 62 - 10
24y = 52
6. Solve for y by dividing both sides by 24:
y = 52/24
y = 13/6 or approximately 2.167
7. Substitute the value of y back into Equation 1 to solve for x:
-2x + 17(13/6) = 31
-2x + 221/6 = 31
-2x = 31 - 221/6
-2x = (186 - 221)/6
-2x = -35/6
8. Solve for x by dividing both sides by -2:
x = (-35/6) / -2
x = (35/6) × (1/-2)
x = -35/12 or approximately -2.917
Therefore, the solution to the system of equations is x ≈ -2.917 and y ≈ 2.167.