Solve using elimination.–x + 5y = –14x − 10y = –16

Sure, let's solve the system of equations using elimination.

The system of equations is:

1. -x + 5y = -14
2. -x - 10y = -16

Step 1: Align the equations

To use elimination, we need to align the equations so that like terms are vertically aligned. The equations are already aligned.

Step 2: Eliminate one variable

We can eliminate x by adding the two equations together:

(-x + 5y) + (-x - 10y) = -14 + -16

This simplifies to:

-2x - 5y = -30

Step 3: Solve for one variable

Now we can solve for x:

-2x = 5y - 30

x = (5y - 30) / -2

x = -2.5y + 15

Step 4: Substitute x in one of the original equations

We can substitute x in the first equation:

-(-2.5y + 15) + 5y = -14

This simplifies to:

2.5y - 15 + 5y = -14

7.5y - 15 = -14

7.5y = 1

y = 1 / 7.5

y = 0.1333

Step 5: Substitute y in the equation found in step 3

x = -2.5(0.1333) + 15

x = -0.3333 + 15

x = 14.6667

So, the solution to the system of equations is x = 14.6667 and y = 0.1333.

Sure, let's solve the system of equations using elimination.

The system of equations is:

1. -x + 5y = -14
2. -x - 10y = -16

Step 1: Align the equations

To use elimination, we need to align the equations so that like terms are vertically aligned. The equations are already aligned.

Step 2: Eliminate one variable

We can eliminate x by adding the two equations together:

(-x + 5y) + (-x - 10y) = -14 + -16

This simplifies to:

-2x - 5y = -30

Step 3: Solve for one variable

Now, we can solve for x by dividing every term by -2:

x + 2.5y = 15

Step 4: Substitute back into one of the original equations

We can substitute x = -2.5y + 15 into the first equation:

-(-2.5y + 15) + 5y = -14

This simplifies to:

2.5y - 15 + 5y = -14

7.5y - 15 = -14

7.5y = 1

y = 1 / 7.5

y = 0.1333

Step 5: Substitute y into the equation from step 3 to solve for x

x + 2.5(0.1333) = 15

x + 0.3333 = 15

x = 15 - 0.3333

x = 14.6667

So, the solution to the system of equations is x = 14.6667 and y = 0.1333.