Question

y = x2 − 2x − 19
y + 4x = 5
The pair of points representing the solution set of this system of equations is (-6, 29) and

Answer 1

y = 5 - 4x

5 - 4x = x^2 - 2x - 19
0 = x^2 + 2x -24
0 = (x + 6)(x - 4)
Therefore x = -6 (Given) or 4

x = 4, y = -9
(4,-9) is the other solution

Answer 2

The other point which is a solution for the given system of equations is (4,-9). This is obtained by applying substitution and factorization methods to the given system of equations.

Solution for the system of equations:

• Solution is the point that satisfies the system of equations
• Solutions for a system of equations can be determined in different ways. some of them are Substitution, Graphing, and Elimination
• Substitution method allows one to substitute an expression w.r.t one variable to solve the other variable
• Elimination method eliminates one variable by adding or subtracting two equations to find the value of the other variable

Solving the system of equations:

Given the system of equations,

$y=x^2-2x-19\\y+4x=5$

Substituting the first equation in the

second equation,

⇒ $x^2-2x-19+4x=5$

On simplifying,

⇒ $x^2+2x-24=0$

The obtained expression is a quadratic equation, then for solving this we use the factorization method

then,

⇒ $x^2+6x-4x-24=0$

⇒ $x(x+6)-4(x+6)=0$

⇒ $(x-4)(x+6)=0$

Thus,

$x=4$ or $x=-6$

Since it is given in the question that one of the solutions in the pair of solutions is (-6,29)

So, we are taking x=4

Substituting x=4 in the second equation, we get

$y+4(4)=5$

⇒ y=5-16

⇒ y=-9

that is (x, y) → (4,-9)

Therefore, the other solution for the given system of equations is (4,-9).

Learn more about the substitution method here:

https://brainly.com/question/13729904

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