Solved on Dec 10, 2023

Solve the system of simultaneous equations $x-9y=10$ and $3y^2=4x+7$ , then show that $3y^2-36y-47=0$ .

STEP 1

Assumptions
1. We have two simultaneous equations: $\begin{aligned} x - 9y &= 10 \quad \text{(Equation 1)} \\ 3y^2 &= 4x + 7 \quad \text{(Equation 2)} \end{aligned}$
2. We need to manipulate these equations to show that $3y^2 - 36y - 47 = 0$ .

STEP 2

Solve Equation 1 for $x$ .
$x = 9y + 10$

STEP 3

Substitute the expression for $x$ from Equation 1 into Equation 2.
$3y^2 = 4(9y + 10) + 7$

STEP 4

Distribute the 4 across the parentheses.
$3y^2 = 36y + 40 + 7$

STEP 5

Combine like terms on the right side of the equation.
$3y^2 = 36y + 47$

STEP 6

Subtract $36y + 47$ from both sides of the equation to set the equation to zero.
$3y^2 - 36y - 47 = 0$
We have shown that $3y^2 - 36y - 47 = 0$ .

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Solve the system of simultaneous equations $x-9y=10$ and $3y^2=4x+7$ , then show that $3y^2-36y-47=0$ .

STEP 1

Assumptions
1. We have two simultaneous equations: $\begin{aligned} x - 9y &= 10 \quad \text{(Equation 1)} \\ 3y^2 &= 4x + 7 \quad \text{(Equation 2)} \end{aligned}$
2. We need to manipulate these equations to show that $3y^2 - 36y - 47 = 0$ .

STEP 2

Solve Equation 1 for $x$ .
$x = 9y + 10$

STEP 3

Substitute the expression for $x$ from Equation 1 into Equation 2.
$3y^2 = 4(9y + 10) + 7$

STEP 4

Distribute the 4 across the parentheses.
$3y^2 = 36y + 40 + 7$

STEP 5

Combine like terms on the right side of the equation.
$3y^2 = 36y + 47$

STEP 6

Subtract $36y + 47$ from both sides of the equation to set the equation to zero.
$3y^2 - 36y - 47 = 0$
We have shown that $3y^2 - 36y - 47 = 0$ .

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Solve the system of simultaneous equations x−9y=10x-9y=10x−9y=10 and 3y2=4x+73y^2=4x+73y2=4x+7, then show that 3y2−36y−47=03y^2-36y-47=03y2−36y−47=0.

STEP 1

STEP 2

Solve Equation 1 for xxx.x=9y+10 x = 9y + 10 x=9y+10

STEP 3

Substitute the expression for xxx from Equation 1 into Equation 2.3y2=4(9y+10)+7 3y^2 = 4(9y + 10) + 7 3y2=4(9y+10)+7

STEP 4

Distribute the 4 across the parentheses.3y2=36y+40+7 3y^2 = 36y + 40 + 7 3y2=36y+40+7

STEP 5

Combine like terms on the right side of the equation.3y2=36y+47 3y^2 = 36y + 47 3y2=36y+47

STEP 6

Subtract 36y+4736y + 4736y+47 from both sides of the equation to set the equation to zero.3y2−36y−47=0 3y^2 - 36y - 47 = 0 3y2−36y−47=0We have shown that 3y2−36y−47=03y^2 - 36y - 47 = 03y2−36y−47=0.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the system of simultaneous equations $x-9y=10$ and $3y^2=4x+7$ , then show that $3y^2-36y-47=0$ .

Solve Equation 1 for $x$ .
$x = 9y + 10$

Substitute the expression for $x$ from Equation 1 into Equation 2.
$3y^2 = 4(9y + 10) + 7$

Distribute the 4 across the parentheses.
$3y^2 = 36y + 40 + 7$

Combine like terms on the right side of the equation.
$3y^2 = 36y + 47$

Subtract $36y + 47$ from both sides of the equation to set the equation to zero.
$3y^2 - 36y - 47 = 0$
We have shown that $3y^2 - 36y - 47 = 0$ .