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Solve each problem by using a system of three equations inthree unknowns.
Working overtime. To make ends meet, Ms. Farns by works three jobs. Her total income last year was 48,000 dollars. Her income from teaching was just 6000 dollars more than her income from house painting. Royalties from her textbook sales were one-seventh of the total money she received from teaching and house painting. How much did she make from each source last year?
$\$ 24,000$ teaching, $\$ 18,000$ painting, $\$ 6000$ royalties
Algebra
Algebra 2
Chapter 4
Systems of Linear Equations
Section 3
Systems of Linear Equations in Three Variables
Polynomials
Systems of Equations and Inequalities
Introduction to Algebra
Graph Linear Functions
Write Linear Equations
Linear Equations and Functions
Matrices and Determinants
University of California, Berkeley
University of North Carolina at Chapel Hill
University of Washington
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So this problem we know that woman works three different jobs teachers paints get royalties. Me, Kotal from these three jobs, 48 $1000 pulled that are teaching brings and $4000 more. That house painting royalties is 17 total of teaching and painting. Now we can use substitution Solve these problems. We have this tea with 4000 plus B so it's plugged that in for tea here. That's gonna give us our equals. 1/7. 4000 plus two p. You cool? 4000 out of seven or seven to go over set of them. So have now every variable in terms of P, so we can plug in and solve for it. We have t which we know is 4000 plus p. He are just 4000 plotted by seven dude amount of my seven p. No, Mrs 48,000. Now we're gonna have to pee close to over seven p 24,000 moms for I wouldn't go out of my seven. So now you're calculators to solve this? Um, we're gonna have 16/7 p equals 44. Four 1000 about seven. Not by 67 where you pee he was 19,000. Once we have P, uh, we can put him quickly. Insult our r is for 4000 out by seven. Plus 2/7 times. 19,000. It's gonna be 6000. Then we know that he has to be 48,000 minus R minus p. All right, that's a car p. So another teaching brings in 23,000. Some clarity over answers. Uh, painting was 90 Doesn't teaching 23,000. You're
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