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lubasha [3.4K]
3 years ago
5

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

Mathematics
1 answer:
REY [17]3 years ago
7 0

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)

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