Question

Can someone help me ? Its due today please

Answer 1

x=3

y=5

Explanation:

Method 1 ; Substitution Method

`3x + 2y =19\\2x+2y=16\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:3x+2y=19:\\\quad x=(19-2y)/(3)\\\\\mathrm{Subsititute\:}x=(19-2y)/(3)\\\begin{bmatrix}2* (19-2y)/(3)+2y=16\end{bmatrix}\\\\Simplify\\\begin{bmatrix}(38+2y)/(3)=16\end{bmatrix}\\\mathrm{Isolate}\:y\:\mathrm{for}\:(38+2y)/(3)=16:\quad y=5\\\\\mathrm{For\:}x=(19-2y)/(3)\\\\Substitute\:y\:= \:5\\x=(19-2*\:5)/(3)\\\\(19-2*\:5)/(3)=3\\\\x=3,\:y=5`

Method 2 : Elimination method

`\begin{bmatrix}3x+2y=19\\ 2x+2y=16\end{bmatrix}\\\\\mathrm{Multiply\:}3x+2y=19\mathrm{\:by\:}2\:\\\mathrm{:}\:\quad \:6x+4y=38\\\\\mathrm{Multiply\:}2x+2y=16\mathrm{\:by\:}3\:\\\mathrm{:}\:\quad \:6x+6y=48\\\\\begin{bmatrix}6x+4y=38\\ 6x+6y=48\end{bmatrix}\\\\6x+6y=48\\-\\\underline{6x+4y=38}\\2y=10\\\\\begin{bmatrix}6x+4y=38\\ 2y=10\end{bmatrix}\\\\\mathrm{Solve}\:2y=10\:\mathrm{for}\:y:\quad y=5\\\mathrm{For\:}6x+4y=38\mathrm{\:plug\:in\:}y=5`

`\mathrm{Solve}\:6x+4*\:5=38\:\mathrm{for}\:x:\quad x=3\\\\x=3,\:y=5`

Answer 2

x=3

y=5

Explanation:

3x+2y=19

- 2x+2y=16

_____________

x=3

3(3)=9

19-9=10

10÷2=5

y=5