Question

Select the pair of (x, y) values that makes the following system of equations true:

y=6x−5
y=−x+9
(1 point)
Responses

(1, 1)
(1, 1)

(2, 7)
(2, 7)

(1, 8)
(1, 8)

(4/5, −1/5)

Answer 1

To find the pair of \((x, y)\) values that satisfies both equations, we can either substitute the \(x\) values from the options into the equations or solve the equations simultaneously.

The two equations are:
1. \(y = 6x - 5\)
2. \(y = -x + 9\)

Let's set them equal to each other to find the intersection point:

\[ 6x - 5 = -x + 9 \]

Now solve for \(x\):
1. Add \(x\) to both sides:
\[ 6x + x - 5 = 9 \]
\[ 7x - 5 = 9 \]

2. Add \(5\) to both sides:
\[ 7x = 14 \]

3. Divide by \(7\):
\[ x = 2 \]

Now, substitute \(x = 2\) back into one of the equations to find \(y\). Using the first equation:

\[ y = 6(2) - 5 = 12 - 5 = 7 \]

So, the point that satisfies both equations is \((2, 7)\).

Thus, the correct answer is **(2, 7)**.