Algebra 1 help please! urgent!?

Question

4. In the following system of linear equations, state how to combine the two equations to obtain one equation with only one variable. 
5x - 4y = 6 
2x + 3y = 2 
Choose one answer. 
a. Multiply the terms in the first equation by 3, the terms of the second equation by 4, and then add the equation.
b. Multiply the terms in the first equation by 2, the terms of the second equation by 5, and then add the equations.
c. Multiply the terms in the first equation by -3, the terms of the second equation by 4, and then add the equations.
d. Add the equations 
5. Choose the ordered pair that is a solution to the system of equations. 
-3x + 2y = 10 
-2x - y = -5 
Choose one answer. 
a. (-2, 5)
b. (2, -5)
c. (0, -5)
d. (0, 5) 


6. Which strategies could be used for solving the following system of equations? 

2x + y = 4 
x - y = 2 
Choose one answer. 
a. Graph both equations on the coordinate plane and find the point of intersection.
b. Solve the first equation for y and then substitute that expression into the second equation.
c. Add the two equations together resulting in an equation with one variable.
d. a, b, and c are all correct. 

Answer 1

• 4).

Elimination method  :

The system of equations : 5x - 4y = 6 → ( 1 )

                                          2x + 3y = 2 → ( 2 ).

To combine the equations (1) & (2) to obtain one equation with only one variable, multiply the terms in first equation by 3, the terms of second equation by 4 and then add the equations.

15x - 12y = 18

8x + 12y = 8

(+)____________

23x = 26

⇒ x = 26/23.

Substitute the value x = 26/23 in eq (1) for y.

5(26/23) - 4y = 6

4y = 130/23 - 6

= (130 - 138)/23

= - 8/23

⇒ y = - 2/23.

The solution is (x, y) = (26/23, - 2/23).

 

Option a is the correct choice.

• 5).

Substitution method  :

The system of equations are - 3x + 2y = 10 and - 2x - y = - 5.

Since the y - coefficient is negative 1, solve equation : - 2x - y = - 5 for y.

- 2x - y = - 5

y = - 2x + 5.

Substitute y = - 2x + 5 in the equation : - 3x + 2y = 10 for x.

- 3x + 2(- 2x + 5) = 10

- 3x - 4x + 10 = 10

- 7x = 0

⇒ x = 0.

Substitute the value x = 0 in y = - 2x + 5 for y.

y = - 2(0) + 5

y = 0 + 5

⇒ y = 5.

The solution of the system (x, y) = (0, 5).

 

Option d is the correct choice.

• 6).

The system of equations are 2x + y = 4 and x - y = 2.

Solve the given system in three methods as follows :

• Graphing method : Graph the given system of equations on the coordinate plane and find the point of intersection.
• Substitution method : Solve the any of two equations for x or y and substitute that expression into the either of given two equations.
• Elimination method : Add the given two equations together resulting in an equation with one variable.

So, option d is the correct choice.