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Chapter 11: Q 209 (page 1147)

In the following exercises, solve the system of equations by using substitution.

y=x2-4y=x-4

Short Answer

Expert verified

The required solutions of given system of equations are :-

0,-4and(1,-3).

Step by step solution

01

Step 1. Given Information 

We have given the following system of equations :-

y=x2-4y=x-4

We have to solve this system of equations. That is we have to find pair for values of xandythat satisfies this system of equations.

We will substitute the value of yfrom second equation in first one. Than we have a quadratic equation inx. After that we will solve the equations, to get required values.

02

Step 2. Substitute value of y

The given system of equations is :-

y=x2-4y=x-4

Substitute the value y=x-4in first equation y=x2-4, then we have :-

x-4=x2-4x=x2x2-x=0

03

Step 3. Solve the quadratic equation 

We have :-

x2-x=0鈬�x(x-1)=0鈬�x=0andx-1=0鈬�x=0andx=1鈬�x=0,1.

04

Step 4. Find values of y

We find :-

x=0,1

Also we have :-

y=x-4.

So that :-

When x=0, y=0-4=-4. So solution pair is 0,-4.

When x=1, y=1-4=-3. So solution pair is1,-3.

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