Question

Find the solution of the system of equations.
10, x, plus, 6, y, equals, 16
10x+6y=
16
minus, 10, x, plus, 5, y, equals, 50
−10x+5y=
50

Answer 1

To solve the system of equations:

1. \( 10x + 6y = 16 \)
2. \( -10x + 5y = 50 \)

We'll use the method of elimination or substitution. First, we can simplify the equations if needed, but in this case, let's just add the two equations together:

First, let's rewrite the given equations clearly:

1. \( 10x + 6y = 16 \) \quad (Equation 1)
2. \( -10x + 5y = 50 \) \quad (Equation 2)

Adding Equation 1 and Equation 2:

\[
(10x + 6y) + (-10x + 5y) = 16 + 50
\]

This simplifies to:

\[
(10x - 10x) + (6y + 5y) = 66
\]

Thus, we have:

\[
0 + 11y = 66
\]

Now, solve for \( y \):

\[
11y = 66
\]

Dividing both sides by 11:

\[
y = 6
\]

Now that we have \( y = 6 \), we can substitute this value back into one of the original equations to find \( x \). Let's use Equation 1:

\[
10x + 6(6) = 16
\]

This simplifies to:

\[
10x + 36 = 16
\]

Subtract 36 from both sides:

\[
10x = 16 - 36
\]

\[
10x = -20
\]

Now, divide by 10:

\[
x = -2
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-2, 6)}
\]