Question

Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x + 5 y = 7 and x + 4y = 17. Based on this information, which statement is correct?

(–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17.
(–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17.
(–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7.
(–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Answer 1

D. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Step-by-step explanation:

The given equations are:

and

Betty correctly determined that the ordered pair is a solution by substituting it into both equations.

Betty's work will look like this;

First Equation:

This statement is True.

Second equation;

This is also TRUE

Hence the correct answer is

D. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Answer 2

Since both equations are satisfied, the point (-3,5) is the solution of the system

Explanation:

System of Equations

If a system of equations of two variables has a single solution (x,y), then both equations must be satisfied for x and y.

We are given the system:

6 x + 5 y = 7

x + 4y = 17

Betty found the solution (-3,5). Substituting in both equations:

6*(-3) + 5 * 5 = -18 + 25 = 7

-3 + 4*20 = 17

Since both equations are satisfied, the point (-3,5) is the solution of the system