Question

!!!!! 60 POINTS !!!!!!!

How would you go about solving this? Please provide an explanation + formulae/rules if needed. Thank you!

Answer 1

Answer:

Step-by-step explanation:

7x+3y=3,3-y=7

7x+3y=3

7x=-3y+3

x=1/7(-3y+3)

x=-3/7y+3

x=-3/7y+3/7

-16/7y=40/7

y=-5/2

x=15/14+3/7

x=3/2

y=-5/2

x=3/2=1 1/2= 1.5

y=-5/2=-2 1/2= -2.5

Answer 2

Answer:

$x = \dfrac{3}{2}$ and $y = -\dfrac{5}{2}$

Step-by-step explanation:

To solve the simultaneous equations:

$\begin{cases} 7x + 3y = 3 \\ 3x - y = 7 \end{cases}$

We can use the method of substitution or elimination. Here, I'll use the elimination method.

Multiply the second equation by 3 to eliminate $y$:

$\begin{cases} 7x + 3y = 3 \\ 9x - 3y = 21 \end{cases}$

Add the equations together:

$(7x + 3y) + (9x - 3y) = 3 + 21$

$7x + 3y + 9x - 3y = 24$

$16x = 24$

Solve for $x$:

$x = \dfrac{24}{16}$

$x = \dfrac{3}{2}$

Substitute $x = \dfrac{3}{2}$ into one of the original equations to solve for $y$. Let's use the first equation:

$7\left(\dfrac{3}{2}\right) + 3y = 3$

$\dfrac{21}{2} + 3y = 3$

$3y = 3 - \dfrac{21}{2}$

$3y = \dfrac{6 - 21}{2}$

$3y = -\dfrac{15}{2}$

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

$y = -\dfrac{5}{2}$

So, the solution to the simultaneous equations is $x = \dfrac{3}{2}$ and $y = -\dfrac{5}{2}$.