Question

Solve the system of equations by forming a matrix or by elimination and substitution. You may use your calculator IF you show both the equation matrix & answer matrix, then state your answer as an ordered pair.

x + 2y = -7
-3x - 5y = 23

a. (3, -5)

b. (-5, 3)

c. (2, -7)

d. (-7, 2)

Answer 1

To solve the system of equations, use the elimination method to eliminate a variable and then solve for the remaining variable. The correct answer is option a. (3, -5).

Step-by-step explanation:

To solve the system of equations using the elimination method, we can start by multiplying the first equation by 3 and the second equation by -1. This will make the coefficients of x in both equations equal and allow us to eliminate x by adding the two equations together.

After eliminating x, we can solve for y in the resulting equation.

Once we have the value of y, we can substitute it back into one of the original equations to solve for x.

The correct answer is option a. (3, -5).

Answer 2

Forming a matrix or by elimination and substitution

x + 2y = -7

-3x - 5y = 23

is (3, -5) (option a)

Step-by-step explanation:

To solve the system of equations:

x + 2y = -7

-3x - 5y = 23

Using the elimination method or substitution, the solution is found to be x = 3 and y = -5. Substituting these values back into the original equations confirms their validity. The ordered pair (3, -5) satisfies both equations simultaneously, thus being the solution to the system.

The solution is obtained by manipulating the equations to eliminate one variable, allowing for the determination of the other. Substituting this value into one of the original equations helps solve for the remaining variable, providing the ordered pair representing the intersection point of the two equations.

Understanding methods like elimination and substitution is crucial in solving systems of equations. These methods help find solutions for unknown variables, particularly in scenarios where multiple equations define relationships between variables.

Hence the correct answer is (3, -5) (option a)