Question

name: ____________________________ date: _____________
solving systems by substitution
n - gen math® algebra i homework
fluency

1. solve each of the following system of equations by substitution.

(a) $y = x + 8$
$y = 4x - 1$
(b) $y = - 3x + 5$
$2x + y = 6$
(c) $4x + 3y = 37$
$y = x - 4$
(d) $x - 5y = - 49$
$y = - 2x + 1$

Explanation:

(a) Step1: Substitute $y=x+8$ into second equation

$x+8=4x-1$

(a) Step2: Solve for $x$

$8+1=4x-x \implies 9=3x \implies x=3$

(a) Step3: Substitute $x=3$ into $y=x+8$

$y=3+8=11$

(b) Step1: Substitute $y=-3x+5$ into second equation

$2x+(-3x+5)=6$

(b) Step2: Simplify and solve for $x$

$2x-3x+5=6 \implies -x=6-5 \implies x=-1$

(b) Step3: Substitute $x=-1$ into $y=-3x+5$

$y=-3(-1)+5=3+5=8$

(c) Step1: Substitute $y=x-4$ into first equation

$4x+3(x-4)=37$

(c) Step2: Expand and solve for $x$

$4x+3x-12=37 \implies 7x=37+12 \implies 7x=49 \implies x=7$

(c) Step3: Substitute $x=7$ into $y=x-4$

$y=7-4=3$

(d) Step1: Substitute $y=-2x+1$ into first equation

$x-5(-2x+1)=-49$

(d) Step2: Expand and solve for $x$

$x+10x-5=-49 \implies 11x=-49+5 \implies 11x=-44 \implies x=-4$

(d) Step3: Substitute $x=-4$ into $y=-2x+1$

$y=-2(-4)+1=8+1=9$

Answer:

(a) $x=3$, $y=11$
(b) $x=-1$, $y=8$
(c) $x=7$, $y=3$
(d) $x=-4$, $y=9$