To solve the system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
From the first equation, we can solve for x:
-x + 6y = 13
x = 13 - 6y
Substituting this expression for x in the second equation:
4(13 - 6y) - 10y = -10
52 - 24y - 10y = -10
52 - 34y = -10
-34y = -62
y = -62 / -34
y = 31/ 17
Now substituting the value of y back into the first equation to solve for x:
-x + 6(31/17) = 13
-17x + 186/17 = 221/17
-17x = 35/17
x = -(35/17) * (1/17)
x = -35/289
Therefore, the solution to the system of equations is x = -35/289 and y = 31/17.
Method 2: Elimination
We can multiply the first equation by 4 and the second equation by 1 to eliminate the x-term:
-4x + 24y = 52
4x - 10y = -10
Adding the two equations together, we eliminate the x-term:
24y - 10y = 52 - 10
14y = 42
y = 42 / 14
y = 3
Substituting this value of y back into the first equation to solve for x:
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 3.
Both methods yield the same solution: x = 5 and y = 3.
Solve the system of equations. –x+6y=13 4x–10y=–10
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