Question

If 4x + 6y = 15 and 6x - 8y = 14, then find the value of 3x-2y

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Answer 1

Answer:

7

Step-by-step explanation:

4x+6y=15

6x-8y=14

3x-2y=?

Let's take 2 common from both

2(2x+3y)=15

2(3x-4y)=14

=>3x-4y=7

if 3x-4y=7

then 3x-2y=?

3x=7+4y

=7+4y-4y

=7

Answer 2

Answer:

$3x-2y = 8$

Step-by-step explanation:

$\textrm{First of all, we have to find the value of }x\textrm{ and }y\textrm{.}$

$\begin{bmatrix}4x+6y=15\\ 6x-8y=14\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:4x+6y=15$

$4x+6y=15$

$\mathrm{Subtract\:}6y\mathrm{\:from\:both\:sides}$

$4x+6y-6y=15-6y$

$\mathrm{Simplify}$

$4x=15-6y$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\dfrac{4x}{4}=\dfrac{15}{4}-\dfrac{6y}{4}$

$\mathrm{Simplify}$

$x=\dfrac{15-6y}{4}$

$\mathrm{Subsititute\:}x=\dfrac{15-6y}{4}$

$\begin{bmatrix}6\cdot \dfrac{15-6y}{4}-8y=14\end{bmatrix}$

$\mathrm{Isolate}\:y\:\mathrm{for}\:6\cdot\dfrac{15-6y}{4}-8y=14$

$6\cdot \dfrac{15-6y}{4}-8y=14$

$\mathrm{Expand\:}6\cdot \dfrac{15-6y}{4}-8y:\quad -17y+\dfrac{45}{2}$

$-17y+\dfrac{45}{2}=14$

$\mathrm{Subtract\:}\dfrac{45}{2}\mathrm{\:from\:both\:sides}$

$-17y+\dfrac{45}{2}-\dfrac{45}{2}=14-\dfrac{45}{2}$

$\mathrm{Simplify}$

$-17y=-\dfrac{17}{2}$

$\mathrm{Divide\:both\:sides\:by\:}-17$

$\dfrac{-17y}{-17}=\dfrac{-\dfrac{17}{2}}{-17}$

$\mathrm{Simplify}$

$y=\dfrac{1}{2}$

$\mathrm{For\:}x=\dfrac{15-6y}{4}$

$\mathrm{Subsititute\:}y=\dfrac{1}{2}$

$x=\dfrac{15-6\cdot \dfrac{1}{2}}{4}$

$\dfrac{15-6\cdot \dfrac{1}{2}}{4}$

$6\cdot \dfrac{1}{2}=3$

$=\dfrac{15-3}{4}$

$\mathrm{Subtract\:the\:numbers:}\:15-3=12$

$=\dfrac{12}{4}$

$\mathrm{Divide\:the\:numbers:}\:\dfrac{12}{4}=3$

$=3$

$x=3$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=\dfrac{1}{2},\:x=3$

$\textrm{Now, as we got the value of x and y, let's plug them in the equation }3x-2y$

$3\left(3\right)-2\left(\dfrac{1}{2}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$=3\cdot \:3-2\cdot \dfrac{1}{2}$

$3\cdot \:3=9$

$2\cdot \dfrac{1}{2}=1$

$=9-1$

$\mathrm{Subtract\:the\:numbers:}\:9-1=8$

$=8$