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HURRY 70 POINTS!! solve the system using substitution. show all work. {4x + 5y = 7 {y = 3x - 10

User Chahal
by
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2 Answers

11 votes

Answer:

(3, -1)

Explanation:

Given

  • 4x + 5y = 7
  • y = 3x - 10

Subbing the value of y

  • 4x + 5(3x - 10) = 7
  • 4x + 15x - 50 = 7
  • 19x = 57
  • x = 3
  • y = 3(3) - 10
  • y = 9 - 10
  • y = -1
  • Solution is (3, -1)
User Merours
by
8.1k points
4 votes

Answer:

  • x = 3
  • y = -1

Solution: (3, -1)

Explanation:

Given equations:


  • 4x + 5y = 7

  • y = 3x - 10

Step-1: Reorganize the equations with "y" on the L.H.S


\rightarrow \left \{ {{4x + 5y = 7} \atop {y = 3x - 10}} \right.


\rightarrow \left \{ {{5y = 7 - 4x} \atop {y = 3x - 10}} \right.


\rightarrow \left \{ {{5y = 7 - 4x} \atop y =-10 + 3x}} \right.

Step-2: Make the x-variables the same on both equations


\rightarrow \left \{ {{3(5y = 7 - 4x)} \atop 4(y =-10 + 3x)}} \right.


\rightarrow \left \{ {{15y = 21 - 12x} \atop 4y =-40 + 12x}} \right.

Step-3: Add the equations


\rightarrow (15y + 4y) = (21 - 40) + (-12x + 12x)


\rightarrow 19y = -19

Step-4: Divide both sides by 19


\rightarrow (19y)/(19) = (-19)/(19)


\rightarrow y = -1

Step-5: Substitute the value of y into any equation


\rightarrow y = 3x - 10


\rightarrow -1 = 3x - 10

Step-6: Simplify the equation


\rightarrow -1 + 10 = 3x


\rightarrow9= 3x

Step-7: Divide 3 both sides


\rightarrow (9)/(3) = (3x)/(3)


\rightarrow x = 3

(Optional) Step-8: Convert the solution(s) into (x, y) form


\rightarrow (x, y) \rightarrow (x = 3; y=-1) \rightarrow (3,-1)

Thus, the value of x and y is 3 and -1. The solution is (3, -1).

User Adween
by
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