Question

elimination with addition and subtraction
question 15 of 15 (1 point) | question attempt: 1 of
solve the following system of equations.
5x + 6y = -5
5x + 3y = 10
x =
y =

Explanation:

Step1: Subtract the two equations

We have the system:

$$
LATEXBLOCK0
$$

Subtract the second equation from the first equation to eliminate \(x\):

$$ (5x + 6y)-(5x + 3y)=-5 - 10 $$

Simplify the left - hand side: \(5x+6y - 5x - 3y=3y\), and the right - hand side: \(-5-10=-15\). So we get \(3y=-15\).

Step2: Solve for \(y\)

Divide both sides of the equation \(3y = - 15\) by 3:
\(y=\frac{-15}{3}=-5\)

Step3: Substitute \(y\) into one of the original equations

Substitute \(y = - 5\) into the second equation \(5x+3y = 10\):
\(5x+3\times(-5)=10\)
Simplify: \(5x-15 = 10\)
Add 15 to both sides: \(5x=10 + 15=25\)

Step4: Solve for \(x\)

Divide both sides of the equation \(5x = 25\) by 5:
\(x=\frac{25}{5}=5\)

Answer:

\(x = 5\), \(y=-5\)