Question

find the solution of the system of equations. 3x - 10y = -46 8x + 10y = 24 answer attempt 1 out of 5 (□,□) submit answer

Explanation:

Step1: Add the two equations to eliminate \( y \)

We have the system:
\[

$$\begin{cases} 3x - 10y = -46 \\ 8x + 10y = 24 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((3x - 10y)+(8x + 10y)=-46 + 24\)
Simplify the left - hand side: \(3x+8x-10y + 10y=11x\)
Simplify the right - hand side: \(-46 + 24=-22\)
So we get the equation \(11x=-22\)

Step2: Solve for \( x \)

From \(11x=-22\), divide both sides by 11:
\(x=\frac{-22}{11}=-2\)

Step3: Substitute \( x = - 2\) into one of the original equations to solve for \( y \)

Let's substitute \( x=-2\) into the second equation \(8x + 10y=24\)
We have \(8\times(-2)+10y = 24\)
First, calculate \(8\times(-2)=-16\)
So the equation becomes \(-16 + 10y=24\)
Add 16 to both sides: \(10y=24 + 16\)
\(24+16 = 40\), so \(10y=40\)
Divide both sides by 10: \(y=\frac{40}{10}=4\)

Answer:

\((-2,4)\)