Question

Is (5,7) a solution to this system of equations? y=3x–8 y=2x–3

Answer 1

To determine if the point (5, 7) is a solution to the system of equations y = 3x - 8 and y = 2x - 3, we can substitute the values of x and y from the point into both equations and check if they are satisfied.

Let's substitute x = 5 and y = 7 into both equations:

For the equation y = 3x - 8:

7 = 3(5) - 8

7 = 15 - 8

7 = 7

The equation is satisfied.

For the equation y = 2x - 3:

7 = 2(5) - 3

7 = 10 - 3

7 = 7

The equation is also satisfied.

Since both equations are satisfied when we substitute x = 5 and y = 7, we can conclude that (5, 7) is indeed a solution to the system of equations y = 3x - 8 and y = 2x - 3.

Answer 2

yes

Explanation:

to determine if (5, 7 ) is a solution substitute the x- coordinate 7 into the right side of both equations.

if the corresponding value of y for both is equal to the y- coordinate 7 then it is a solution to the system.

y = 3(5) - 8 = 15 - 8 = 7 ← equals y- coordinate

y = 2(5) - 3 = 10 - 3 = 7 ← equals y- coordinate

since both equations are true then (5, 7 ) is a solution to the system