Question

Solve{(x,+,2y,=,9),(y,=,-2x):}

Systems of equations

Solve $$\displaystyle{\left\lbrace\begin{matrix}{x}&+&{2}{y}&=&{9}\\{y}&=&-{2}{x}\end{matrix}\right.}$$

2021-02-01

Substitute equation (1) into equation (2) and solve for x.

$$x + 2(-2x) = 9 x - 4x = 9 -3x = 9 x = -3$$

Substitute $$x = -3$$ into equation (2) and solve for y.

$$y = -2 \times (-3) y = 6$$

Thus, the solution is (-3, 6).