Question

Solve the system of equations. 2x-y=6 x^{2}+y=9

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ANSWERED
asked 2021-03-23
Solve the system of equations.
2x-y=6
\(\displaystyle{x}^{{{2}}}+{y}={9}\)

Answers (1)

2021-03-25
Step 1
Given the system of equations
2x-y=6...(1)
\(\displaystyle{x}^{{{2}}}+{y}={9}\)...(2)
To solve the equation:
Step 2
We use the substitution method to solve, from equation (1),
y=2x-6...(3)
Now, substitute in equation (2) and solve for x,
\(\displaystyle{x}^{{{2}}}+{\left({2}{x}-{6}\right)}={9}\)
\(\displaystyle{x}^{{{2}}}+{2}{x}-{6}={9}\)
\(\displaystyle{x}^{{{2}}}+{2}{x}-{15}={0}\)
\(\displaystyle{x}^{{{2}}}+{5}{x}-{3}{x}-{15}={0}\)
x(x+5)-3(x+15)=0
(x-3)(x+5)=0
\(\displaystyle\therefore{x}={3},-{5}\)
Step 3
Find the value of y corresponding to x,
Substitute the value of x as 3 in y,
y=2(3)-6=6-6=0
Substitute the value of x as -5 in y,
y=2(-5)-6=-10-6=-16
Step 4
Answer:
Thus, the solution of the given system is (3,0) and (-5,-16).
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