Question

Solve the following system of equations by elimination. SHOW ALL YOUR WORK (4 points)-3x - 3y=93x - 4y = 5

Answer 1

x = -1 and y = -2.

Explanation:

As per the question, Ahmod given the two equation which should solve by elimination method. Okay, let us use the method.

Let,

`{ \red{ \sf{ - 3x - 3y = 9}}} \: { \to} \: { \tt{ {eq}^(n) (1)}}`

`{ \red{ \sf{ \: \: \: 3x - 4y = 5}}} \: { \to} \: { \tt{ {eq}^(n) (2)}}`

____________________

`{ \red{ \sf{ \: \: \: \: \: \: \: \: - 7y = 14}}}`

`{ \red{ \sf{ \: \: \: \: \: \: \: \: \: \: \: y = - (14)/(7)}}}`

`{ \red{ { \sf{ \: \: \: \: \: \: \: \: \: \: \:y = - 2}}}}`

Substitute the value of y in Eqⁿ (1)

`{ \green{ \sf{ - 3x - 3( - 2) = 9}}}`

`{ \green{ \sf{ - 3x + 6 = 9}}}`

`{ \green{ \sf{ - 3x = 9 - 6}}}`

`{ \green{ \sf{ - 3x = 3}}}`

`{ \green{ \sf{x = - (3)/(3)}}}`

`{ \blue{ \boxed{ \sf{x = - 1}}}}`

Answer 2

-3x - 3y=9 (1)

+ 3x - 4y = 5 (2) First, Add equation 1 to equation 2

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0 - 7y = 14 Then, isolate y

y= 14/ -7 = -2

Replace y in equation 2 or equation 1. Let's replace in equation 2

3x - 4(-2)= 5

3x + 8 = 5 Isolating 3x

3x = 5-8

3x = -3 Isolating x

x = -3/3= -1

Answer: y= -2 and x=-1