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NO LINKS!! Use the method of substitution to solve the system. (if there's no solution, enter no solution). Part 3z​

NO LINKS!! Use the method of substitution to solve the system. (if there's no solution-example-1

2 Answers

6 votes

Answer:


(x,y)=\left(\; \boxed{-13,4} \; \right)\quad \textsf{(smaller $x$-value)}


(x,y)=\left(\; \boxed{3,0} \; \right)\quad \textsf{(larger $x$-value)}

Explanation:

Given system of equations:


\begin{cases}\;\;\;\;\;\;\;y^2=3-x\\x+4y=3\end{cases}

To solve by the method of substitution, rearrange the second equation to make x the subject:


\implies x=3-4y

Substitute the found expression for x into the first equation and rearrange so that the equation equals zero:


\begin{aligned}x=3-4y \implies y^2&=3-(3-4y)\\y^2&=3-3+4y\\y^2&=4y\\y^2-4y&=0\end{aligned}

Factor the equation:


\begin{aligned}\implies y^2-4y&=0\\y(y-4)&=0\end{aligned}

Apply the zero-product property and solve for y:


\implies y=0


\implies y-4=0 \implies y=4

Substitute the found values of y into the second equation and solve for x:


\begin{aligned}y=0 \implies x+4(0)&=3\\x&=3\end{aligned}


\begin{aligned}y=4 \implies x+4(4)&=3\\x+16&=3\\x&=-13\end{aligned}

Therefore, the solutions are:


(x,y)=\left(\; \boxed{-13,4} \; \right)\quad \textsf{(smaller $x$-value)}


(x,y)=\left(\; \boxed{3,0} \; \right)\quad \textsf{(larger $x$-value)}

User Oy
by
7.4k points
1 vote

Answer:

  • (- 9, 4)
  • (3, 0)

=====================

Given system

  • y² = 3 - x
  • x + 4y = 3

Rearrange equations

  • x = 3 - y²
  • x = 3 - 4y

Solve by elimination

  • y² = 4y
  • y² - 4y = 0
  • y(y - 4) = 0
  • y = 0 and y = 4

Find the value of x

  • y = 0x = 3 - 0 = 3
  • y = 4x = 3 - 4*3 = 3 - 12 = - 9
User Joel Cox
by
8.3k points

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