Question

Is (2, 3) a solution to this system of equations?

y = -2x + 7
y = x + 1
yes
no

Answer 1

Yes.

Explanation:

(2, 3) means we'll let x be 2 and y be 3. Let's solve both equations first:

y = -2x + 7

3 = -2(2) + 7

3 = -4 + 7

:. 3 = 3

Okay, so one half is proven. Let's do the other half now.

y = x + 1

3 = 2 + 1

3 = 3

:. (2,3) is a solution to the system of equations.

Answer 2

To determine if (2, 3) is a solution to the system of equations y = -2x + 7 and y = x + 1, we need to check if the values of x and y in the point (2, 3) satisfy both equations.

For the point (2, 3), we have x = 2 and y = 3. Substituting these values into the first equation, we get:

y = -2x + 7
3 = -2(2) + 7
3 = 3

This equation is true, so the point (2, 3) satisfies the first equation.

Substituting x = 2 and y = 3 into the second equation, we get:

y = x + 1
3 = 2 + 1
3 = 3

This equation is also true, so the point (2, 3) satisfies the second equation.

Since the point (2, 3) satisfies both equations in the system, we can conclude that it is a solution to the system. Therefore, the answer is yes.