Question

# Solve the system of equations.{(x,+,4y,=,-2),(-2x,+12y,=,9):}

Systems of equations

Solve the system of equations. $$\{(x,+,4y,=,-2),(-2x,+12y,=,9):\}$$

2021-02-20

$$\{(x,+,4y,=,-2),(-2x,+12y,=,9):\}$$

Multiply equation (1) by 2 $$\{(2x,+,8y,=,-4),(-2x,+12y,=,9):\}$$

Add (1) and (2) $$20y = 14 y = \frac{14}{20} y = \frac{7}{10}$$

Subtitute $$y = \frac{7}{10}$$ into equation (1)

$$x = -2 – 4y x = -2 – \frac{28}{10} x = - 2 – \frac{14}{5} x = -\frac{24}{5}$$

Thus, the answer is $$(-\frac{24}{5} , \frac{7}{10})$$