Question is "solve each of the following systems using SUBSTITUTION METHOD

3) x2+ y2 - x + 3y - 42 = 0 X+y=4

REY [17]

The solution is $(-1,5)$ and $(7,-3)$

Step-by-step explanation:

The expression is $x^{2} +y^{2} -x+3y-42=0$ and $x+y=4$

Using substitution method we can solve the expression.

Let us substitute $x=4-y$ in $x^{2} +y^{2} -x+3y-42=0$

$(4-y)^{2} +y^{2} -(4-y)+3y-42=0$

Expanding and simplifying the expression, we get,

$\begin{array}{r}{16-8 y+y^{2}+y^{2}-4+y+3 y-42=0} \\{2 y^{2}-4 y-30=0}\end{array}$

Let us use the quadratic equation formula to solve this equation,

$\begin{aligned}y &=\frac{4 \pm \sqrt{16-4(2)(-30)}}{2(2)} \\&=\frac{4 \pm \sqrt{16+240}}{4} \\&=\frac{4 \pm 16}{4} \\y &=1 \pm 4\end{aligned}$

Thus, $y=5$ and $y=-3$

Substituting y-values in the equation $x+y=4$ , we get the value of x.

For $y=5$ ⇒ $x=4-5=-1$

For $y=-3$ ⇒ $x=4+3=7$

Thus, the solution set is $(-1,5)$ and $(7,-3)$

7 0

4 years ago

Plzzzzzzzz HELP!!!!!!

sveta [45]

It should be =8.32362

3 0

3 years ago

Nathaniel builds birds and birdhouses using Lego blocks. Let B represent the number of birds and H represent the number of birdh

N76 [4]

Answer:

At-most 3 birdhouses.

Step-by-step explanation:

Let B represent the number of birds and H represent the number of birdhouses that Nathaniel can build with his Lego blocks.

We have been given that Nathaniel builds birds and birdhouses using Lego blocks. The inequality $43B+215H\leq3000$ represents the number of birds and birdhouses Nathaniel could build.

To find the number of birdhouses that Nathaniel can build after making 50 birds, we will substitute B=50 in our given inequality and then solve for H.

$43*50+215H\leq3000$

$2150+215H\leq3000$

Let us subtract 2150 from both sides of our inequality.

$2150-2150+215H\leq3000-2150$

$215H\leq850$

Let us divide both both sides of our inequality by 215.

$\frac{215H}{215}\leq\frac{850}{215}$

$H\leq3.953488$

As Nathaniel can make build less than or equal to 3.953488 and the biggest integer less than or equal to 3.953 is 3, therefore, Nathaniel can build at-most 3 birdhouses with remaining Lego blocks.

3 0

3 years ago

Read 2 more answers

Find the interest due on $950 at 13% for 120 days.

exis [7]

950 x 13 /100 x 120/365 = $ 40.60. Hope that's helpful.

7 0

3 years ago

Read 2 more answers

Part 2: Solve the following word problem. Show all work to receive full credit..

lys-0071 [83]

The numerical representation and final elevation of the fish relative to sea level are :