Mathematics: Solve the system of equations by any method. 5x+9y =16 x+2y =4

Solve the system of equations by any method.

itzyougirllona47

10.02.2022

The system of equations has one solution at (-4, 4).

Step-by-step explanation:

We are given the system of equations:

$\displaystyle\left \{ {{5x+9y=16} \atop {x+2y=4}} \right.$

We can use elimination to solve this system. We need to multiply the second equation by -5 so we can cancel out our x-terms.

$-5\times(x+2y=4) \rightarrow -5x - 10y = -20$

Therefore, our system now becomes:

$\displaystyle\left \{ {{5x+9y=16} \atop {-5x-10y=-20}} \right.$

Now, we can add these two equations together and solve for y.

$\displaystyle(5x + 9y) + (-5x - 10y) = 0 - y\\\\16 + (-20) = -4\\\\-y = -4\\\\\frac{-y}{-1}=\frac{-4}{-1}\\\\y = 4$

Now, we can substitute our value for y into one of the equations and solve for x.

$x+2(4)=4\\\\x + 8 = 4\\\\x = -4$

Therefore, our final solution is (-4, 4).

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