Question

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

Answer 1

Answer:

• x = 3
• y = -1

Solution: (3, -1)

Step-by-step 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

$\rightarrow \dfrac{19y}{19} = \dfrac{-19}{19}$

$\rightarrow y = -1$

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

$\rightarrow \dfrac{9}{3} = \dfrac{3x}{3}$

$\rightarrow x = 3$

(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).

Answer 2

Answer:

(3, -1)

Step-by-step 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)