Question

3 multiple choice 2 points
what is the value of the y - coordinate of the solution to the system of equations ( x - 2y = 1 ) and ( x + 4y = 7 )?
( \bigcirc ) 4
( \bigcirc ) 3
( \bigcirc ) ( -1 )
( \bigcirc ) 1

4 multiple choice 2 points
using the substitution method, ken solves the following system of equations algebraically.
( \begin{cases}2x - y = 5\\3x + 2y = -3end{cases} )
which equivalent equation could ken use?
( \bigcirc ) ( 3x + 2(2x - 5) = -3 )
( \bigcirc ) ( 3left( \frac{5}{2} - y
ight) + 2y = -3 )
( \bigcirc ) ( 3left( y + \frac{5}{2}
ight) + 2y = -3 )
( \bigcirc ) ( 3x + 2(5 - 2x) = -3 )

Explanation:

Question 3

Step1: Eliminate $x$ via subtraction

Subtract first eq from second:
$$(x + 4y) - (x - 2y) = 7 - 1$$

Step2: Simplify to solve for $y$

$$6y = 6$$
$$y = \frac{6}{6} = 1$$

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Question 4

Step1: Isolate $y$ from first equation

Rearrange $2x - y = 5$:
$$y = 2x - 5$$

Step2: Substitute into second equation

Replace $y$ in $3x + 2y = -3$:
$$3x + 2(2x - 5) = -3$$

Answer:

1