Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 7 - Polynomial Equations and Factoring - 7.6 - Factoring ax^2 + bx + c = 0 - Exercises - Page 396: 53

Answer

The solution is $(-1,-4)$. Check: Both first and second equations are satisfied when we put the solution in the equations. $-4=3+7(-1)=-4$ and $-4-(-1)=-4+1=-3$

Work Step by Step

Given: $y=3+7x$ and $y-x=-3$. From the second equation, we have $y=x-3$. Substituting this in the first equation, we get $(x-3)=3+7x$ $\implies 7x-x=-3-3$ or $6x=-6$ $\implies x=-1$ Putting the value of $x$ in the first equation, we obtain $y=3+7(-1)=3-7=-4$. The solution is $(-1,-4)$. Check: Both first and second equations are satisfied when we put the solution in the equations. $-4=3+7(-1)=-4$ and $-4-(-1)=-4+1=-3$
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