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Chapter 4: Q 37. (page 386)

Solve the system of equations by substitution

3x+4y=1y=-25x+2

Short Answer

Expert verified

The solution for the system of equations is,

x=-5y=4

Step by step solution

01

Step 1. Given the information

The system of equations is,

3x+4y=1y=-25x+2

02

Step 2. Substituting the value of y in the equation.

Substituting y=-25x+2in the equation,

3x+4y=1

role="math" localid="1644342937459" 3x+4(-25x+2)=1

3x-85x+8=1

3x-8x5=1-8

15x-8x5=-7

7x5=-7

x=-7梅75

x=-7脳57

x=-5

03

Step 3. Substituting the value of x in the equation

Substituting x=-5in the equation

y=-25x+2

y=-25(-5)+2

y=2+2

y=4

04

Step 4. Checking the solution for the equation 3x+4y=1

Substituting x=-5y=4in the equation

3x+4y=1

3(-5)+4(4)=1

-15+16=1

1=1

This is true

05

Step 5. Checking the solution for the equation y=-25x+2

Substituting x=-5y=4in the equation

y=-25x+2

4=-25(-5)+2

4=2+2

4=4

This is true.

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