Question

Use substitution to solve the following system of equations. What is the value of y? {3x+2y=12{5x−y=7 A) y = -3B) y = 3C) y = -2D) y = 2

Answer 1

y=3

Step-by-step explanation:

Got it right :/

Answer 2

B) y = 3

Explanation

Given the system of equations:

`\begin{gathered} 3x+2y=12\text{ \lparen eq. 1\rparen} \\ 5x-y=7\text{ \lparen eq. 2\rparen} \end{gathered}`

Isolating x from equation 1:

`\begin{gathered} 3x+2y-2y=12-2y \\ 3x=12-2y \\ (3x)/(3)=(12-2y)/(3) \\ x=(12)/(3)-(2)/(3)y \\ x=4-(2)/(3)y\text{ \lparen eq. 3\rparen} \end{gathered}`

Substituting equation 3 into equation 2 and solving for y:

`\begin{gathered} 5(4-(2)/(3)y)-y=7 \\ 5\cdot4-5\cdot(2)/(3)y-y=7 \\ 20-(10)/(3)y-y=7 \\ 20-(13)/(3)y=7 \\ 20-(13)/(3)y-20=7-20 \\ -(13)/(3)y=-13 \\ (-(3)/(13))\cdot-(13)/(3)y=(-(3)/(13))\cdot-13 \\ y=3 \end{gathered}`