Question

Solve the system of equations. \begin{aligned} &-5y+6x = 40 \\\\ &3y-8x=-46 \end{aligned} ​ −5y+6x=40 3y−8x=−46 ​ x=x=x, equals y=y=y, equals

Answer 1

Answer:

The solution is $(5,-2)$ that is, $x=5$ and $y=-2$

Step-by-step explanation:

The given system of equations is

$\left \{ {{-5y+6x=40} \atop {3y-8x=-46}} \right.$

We can solve this system by elimination, that is, we have to eliminate one variable to find the other one.

We are gonna multiply the second equation by $\frac{6}{8}$ and solve for $y$

$\left \{ {{-5y+6x=40} \atop {\frac{18}{8} y-6x=-\frac{276}{8} }} \right.\\\\-5y + \frac{18}{8}y=40-\frac{276}{8}\\-5y+\frac{9}{4}y=40-\frac{69}{2}\\\frac{-20y+9y}{4}=\frac{80-69}{2}\\ \frac{-11y}{4}=\frac{11}{2} \\y=\frac{4(11)}{2(-11)} \\y=-2$

Now, we replace this value in one equation to find the other value

$-5y+6x=40\\-5(-2)+6x=40\\10+6x=40\\6x=40-10\\x=\frac{30}{6}=5$

Therefore, the solution is $(5,-2)$ that is, $x=5$ and $y=-2$

Answer 2

Answer:

x=0

y=-3

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Step-by-step explanation: