Question

solve the system of linear system by substitution.

1. ( 2x + 4y = 12 )

( x = 3y + 1 )
solution:
( x = )
( y = )

1. ( x = 2y + 11 )

( -7x - 2y = -13 )
solution:
( x = )
( y = )

Explanation:

Step1: Substitute $x$ into first equation

Substitute $x=3y+1$ into $2x+4y=12$:
$2(3y+1)+4y=12$

Step2: Simplify and solve for $y$

Expand and combine like terms:
$6y+2+4y=12$
$10y+2=12$
$10y=10$
$y=1$

Step3: Find $x$ using $y=1$

Substitute $y=1$ into $x=3y+1$:
$x=3(1)+1=4$

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Step1: Substitute $x$ into second equation

Substitute $x=2y+11$ into $-7x-2y=-13$:
$-7(2y+11)-2y=-13$

Step2: Simplify and solve for $y$

Expand and combine like terms:
$-14y-77-2y=-13$
$-16y-77=-13$
$-16y=64$
$y=-4$

Step3: Find $x$ using $y=-4$

Substitute $y=-4$ into $x=2y+11$:
$x=2(-4)+11=3$

Answer:

For problem 6:

$x=4$, $y=1$

For problem 7:

$x=3$, $y=-4$