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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