Question

what value of y satisfies the system of equations below?
2x - y = 6
2x + 3y = 14
○ 4
○ 2
○ 5
○ 10

question 3
solve the system by elimination. show all work.
3x + y = 19
2x - y = 6
○ (4, 5)
○ (5, 14)
○ (5, 4)
○ (14, 5)

Explanation:

First System of Equations (Finding y)

Step1: Subtract equations to eliminate $x$

$(2x + 3y) - (2x - y) = 14 - 6$
Simplify: $2x + 3y - 2x + y = 8$ → $4y = 8$

Step2: Solve for $y$

$y = \frac{8}{4}$

Step1: Add equations to eliminate $y$

$(3x + y) + (2x - y) = 19 + 6$
Simplify: $3x + y + 2x - y = 25$ → $5x = 25$

Step2: Solve for $x$

$x = \frac{25}{5} = 5$

Step3: Substitute $x=5$ into $2x - y = 6$

$2(5) - y = 6$ → $10 - y = 6$

Step4: Solve for $y$

$y = 10 - 6 = 4$

Answer:

2

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Second System of Equations (Elimination Method)