Solve the system of equations -x+6y=13 and 4x-10y=-10
To solve the system of equations -x + 6y = 13 and 4x - 10y = -10, we can use the method of substitution or elimination.
Let's use the method of substitution:
From the first equation, we can express x in terms of y:
-x + 6y = 13
=> x = 6y - 13
Now substitute x in the second equation:
4x - 10y = -10
=> 4(6y - 13) - 10y = -10
=> 24y - 52 - 10y = -10
=> 14y - 52 = -10
=> 14y = -10 + 52
=> 14y = 42
=> y = 42/14
=> y = 3
Now substitute y back into the first equation to find x:
-x + 6y = 13
=> -x + 6(3) = 13
=> -x + 18 = 13
=> -x = 13 - 18
=> -x = -5
=> x = 5
Therefore, the solution to the system of equations -x + 6y = 13 and 4x - 10y = -10 is x = 5 and y = 3.
Step 1: We will use the method of substitution to solve the given system of equations.
Step 2: Rearrange the first equation to solve for x in terms of y:
-x + 6y = 13
-x = -6y + 13
x = 6y - 13
Step 3: Substitute the value of x in the second equation with 6y - 13:
4(6y - 13) - 10y = -10
24y - 52 - 10y = -10
24y - 10y = -10 + 52
14y = 42
y = 42/14
y = 3
Step 4: Substitute the value of y in the first equation:
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5
Step 5: The solution to the system of equations is x = 5 and y = 3.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.
Step 1: Multiply the first equation by 4 and the second equation by -1 to make the coefficients of x in both equations the same. This will allow us to eliminate x.
Multiplying the first equation by 4:
4(-x + 6y) = 4(13)
-4x + 24y = 52 (Equation 1)
Multiplying the second equation by -1:
-1(4x - 10y) = -1(-10)
-4x + 10y = 10 (Equation 2)
Step 2: Add Equation 1 and Equation 2 together to eliminate x:
(-4x + 24y) + (-4x + 10y) = 52 + 10
-8x + 34y = 62 (Equation 3)
Step 3: Solve Equation 3 for y:
-8x + 34y = 62
34y = 8x + 62
y = (8/34)x + (62/34)
Simplifying further:
y = (4/17)x + (31/17) (Equation 4)
Step 4: Substitute Equation 4 back into one of the original equations to solve for x. Let's use the first equation:
-x + 6y = 13
-x + 6((4/17)x + (31/17)) = 13
-x + (24/17)x + (186/17) = 13
Combining like terms:
(24/17)x - x = 13 - (186/17)
(24/17 - 17/17)x = (221/17 - 186/17)
(7/17)x = 35/17
Multiply both sides by (17/7) to isolate x:
x = (35/17) * (17/7)
x = 5
So, the solution to the system of equations is x = 5.
Step 5: Substitute the value of x back into Equation 4 to solve for y:
y = (4/17)x + (31/17)
y = (4/17)*5 + (31/17)
y = 20/17 + 31/17
y = 51/17
Therefore, the solution to the system of equations is x = 5 and y = 51/17.