To solve the system of equations:
–x + 6y = 13 [Equation 1]
4x – 10y = –10 [Equation 2]
First, let's find a suitable way to eliminate one of the variables by manipulating the equations. We can multiply Equation 1 by 4 to prepare it for elimination with Equation 2:
(–x + 6y = 13) * 4 gives us:
–4x + 24y = 52 [Equation 3, which is Equation 1 multiplied by 4]
Now we have:
–4x + 24y = 52 [Equation 3]
4x – 10y = –10 [Equation 2]
When we add Equation 3 and Equation 2, we can eliminate the x variable:
–4x + 4x + 24y – 10y = 52 – 10
0x + 14y = 42
Now, solve for y:
14y = 42
y = 42 / 14
y = 3
Now we have the value of y, we can plug it into either Equation 1 or Equation 2 to find x. Let's plug it into Equation 1:
–x + 6y = 13
–x + 6(3) = 13
–x + 18 = 13
Subtract 18 from both sides:
–x = 13 – 18
–x = –5
Now, solve for x:
x = 5
Now we have both values:
x = 5
y = 3
So the solution to the system of equations is the point (5, 3).
Solve the system of equations.
–x+6y=13
4x–10y=–10 (1 point)
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WITH THE CORRECT AND SIMPLIFIED ANSWERS
1 answer