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Chapter 5: Q. 5.26 (page 599)

Solve the system by substitution.

x+3y=104x+y=18

Short Answer

Expert verified

The solution set is (4,2).

Step by step solution

01

Step 1. Given Information

We have to solve the system by substitution.

x+3y=104x+y=18

02

Step 2. Firstly solve the equation x+3y=10 for the variable src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOndycz0iaHR0cDovL3d3dy53aXJpcy5jb20veG1sL21hdGhtbC1leHRlbnNpb24iIGhlaWdodD0iMTkiIHdpZHRoPSIxMCIgd3JzOmJhc2VsaW5lPSIxNSI+PCEtLU1hdGhNTDogPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48L21hdGg+LS0+PGRlZnM+PHN0eWxlIHR5cGU9InRleHQvY3NzIi8+PC9kZWZzPjx0ZXh0IGZvbnQtZmFtaWx5PSJBcmlhbCIgZm9udC1zaXplPSIxNiIgZm9udC1zdHlsZT0iaXRhbGljIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiB4PSI0LjUiIHk9IjE1Ij54PC90ZXh0Pjwvc3ZnPg==" role="math" localid="1648476788711" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/d6a55f08-1b94-47a8-ab78-6e0c0ec2fe36.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220328%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220328T142146Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=eef95b6eaa6a4bab4bd2afa045a96380c78406f50d0a2f1988948ca1838f25a0" x.

Subtract3yonbothsidex+3y-3y=10-3yx=10-3y

03

Step 3. Putting the value of x in the second equation.

4(10-3y)+y=1840-12y+y=1840-11y=18Subtract40onbothside40-11y-40=18-40-11y=-22Divideby-11onbothside-11-11y=-22-11y=2

04

Step 4. Now putting y=2 on the equation x=10-3y

x=10-3×2x=10-6x=4

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