Question

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

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

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