Algebra 2 question help please...??

Question

Solve The System by the method of substitution

1. {-5x - y = 7, 2x - 3y = 4}

a. (1, 2)
b. (-1,-2)
c. (-2,-1)
d. (2,1)

2. {5x - y = 10, 4x - y = 7}

a. (3,5)
b. (-5,-3)
c. (5, 3)
d. (-3, -5)

Answer 1

"Substitution" means just that.
Isolate one variable from either equation

1) Answer is B (-1, -2)

ie. since -5x - y = 7 then
-y = 7 + 5x
y = -7 - 5x or -5x - 7 (variables first)

use that in place of the variable y in wither equation so that all your variables are the same (ie. all x in this case)
then simplify using your rules for solving equations with one variable

2x - 3(-5x - 7) =4
2x + 15x + 21 = 4
17x +21 = 4
17X = -17
therefore x = -1 (remember that)

since you know what the value of one variable is, substitute
that in place of it in the equations and solve for the other variable:

if x = -1 then

-5X - y = 7
-5 (-1) - y = 7
5 - y = 7
-y = 7-5
-y = 2
so
y = -2

then use x = -1 and y = -2 as the values in BOTH original equations to check if you are correct. (you should always check ALL equations in a system. Sometimes it works in one but not all...


2.) Follow similar steps
Answer is A ((3,5)

5x - y =10
-y = 10 - 5x
-y = -5x +10
y = 5x - 10

substitute:

4x - y = 7
4x - (5x -10) = 7
4x - 5x +10 = 7
-1x +10 = 7
-1x = -3
x = 3

if x =3 then

5x - y =10
5 (3) - y =10
15 - y =10
-y = -5
y = 5

(3,5)

check in both, it works.

Answer 2

1b. (-1,-2)

2a. (3,5)

Hint:
use trial and error method
for question 1 try
x=-1
y=-2

satisfies both given equations