Question

Solve the following system using the substitution method. Enter your answer as an ordered pair in the form ( x, y).3x - 2y = - 145x + 10y = 30

Answer 1

(-2, 4)

Explanation:

The given equations:

3x - 2y = - 14 ...(1)

5x + 10y = 30 ...(2)

Using substitution method:

From equation 1:

3x - 2y = -14

3x = 2y - 14

$\begin{gathered} \text{divide both sides by 3:} \\ x=\frac{2y}{3}-\frac{14}{3} \end{gathered}$

substitute for y in equation 2:

$\begin{gathered} 5(\frac{2y}{3}\text{ - }\frac{14}{3})\text{ + 10y = 30} \\ \frac{10y}{3}\text{ - }\frac{70}{3}\text{ + 10y = 30} \\ \text{Multiply by 3:} \\ 3(\frac{10y}{3})\text{ -3( }\frac{70}{3}\text{ )+ 3(10y) = 3(30)} \\ 10y\text{ - 70 + 30y = 90} \end{gathered}$$\begin{gathered} \text{collect like terms:} \\ 10y\text{ + 30y - 70 = 90} \\ 40y\text{ - 70 = 90} \\ 40y\text{ = 90 + 70} \\ 40y\text{ = 160} \\ \text{divide both sides by 40:} \\ \frac{40y}{40}=\frac{160}{40} \\ y\text{ = 4} \end{gathered}$

substitute for y in equation 1:

$\begin{gathered} 3x\text{ - 2(4) = -14} \\ 3x\text{ - 8 = -14} \\ \text{add 8 to both sides:} \\ 3x\text{ = -14 + 8} \\ 3x\text{ = -6} \end{gathered}$$\begin{gathered} \text{divide both sides by 3:} \\ \frac{3x}{3}\text{ = }\frac{-6}{3} \\ x\text{ = -2} \end{gathered}$

The solution in ordered pair (x, y) is (-2, 4)