If the equations -9x + y = 17 and 9x + y = 17 are graphed in the xy-plane, at what point (x, y) do the graphs intersect?

If the equations -9x + y = 17 and 9x + y = 17 are graphed in the xy-plane, at what point... | SAT Systems of two linear equations in two variables Practice

Answer: A. $(0, 17)$

Explanation:

$1$ . Set up the system of equations:

- Equation 1: $-9x + y = 17$

- Equation 2: $9x + y = 17$

$2$ . Use the elimination method to solve for y:

- Notice that the x-coefficients are opposites ( $-9$ and $9$ ). Adding the two equations together will eliminate x.

$(-9x + y) + (9x + y) = 17 + 17$

$2y = 34$

- Divide by $2$ :

$y = 17$

$3$ . Solve for x:

- Substitute the value of y ( $17$ ) into either of the original equations. Let's use Equation 2.

$9x + 17 = 17$

- Subtract $17$ from both sides:

$9x = 0$

- Divide by $9$ :

$x = 0$

$4$ . State the intersection point:

- The solution to the system is the point $(x, y)$ , which is $(0, 17)$ .

$5$ . Conclusion:

- The graphs intersect at the point $(0, 17)$ , which matches option A.