Solve the system of equations.

Question

–x+6y=13
4x–10y=–10 (1 point)
(
,
)
WITH THE CORRECT AND SIMPLIFIED ANSWERS

Answer 1

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).