Question

X-2y = 10 x + 3y = 5 Using elimination method

Answer 1

Answer:

The solution to the system of equations be:

• (x, y) = (8, -1)

Step-by-step explanation:

Given the system of equations

$x-2y = 10$

x + 3y = 5

Solving the system of equations using the elimination method

$\begin{bmatrix}x-2y=10\\ x+3y=5\end{bmatrix}$

subtracting the equations

$x+3y=5$

$-$

$\underline{x-2y=10}$

$5y=-5$

solving 5y = -5 for y

$5y=-5$

Divide both sides by 5

$\frac{5y}{5}=\frac{-5}{5}$

Simplify

$y=-1$

For x - 2y = 10 plug in y = -1

$x-2\left(-1\right)=10$

Apply rule  -a(-a) = a

$x+2\cdot \:1=10$

Multiply the numbers:  $2\cdot \:1=2$

$x+2=10$

subtract 2 from both sides

$x+2-2=10-2$

Simplify

$x=8$

Therefore, the solution to the system of equations be:

• (x, y) = (8, -1)

The graph of the solution to the system of equations is also attached below.