Question

mination with addition and subtraction
question 5 of 15 (1 point) | question attempt: 1 of 3
2 3 4 5
solve the following system of equations.
3x + 5y = 5
7x + 5y = 25
x =
y =

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 3x + 5y = 5 \\ 7x + 5y = 25 \end{cases}$$

Subtract the first equation from the second equation to eliminate \(y\):
\((7x + 5y)-(3x + 5y)=25 - 5\)
Simplify the left - hand side: \(7x+5y - 3x - 5y=4x\), and the right - hand side: \(20\). So we get \(4x = 20\).

Step2: Solve for \(x\)

Divide both sides of the equation \(4x = 20\) by \(4\):
\(x=\frac{20}{4}=5\)

Step3: Substitute \(x = 5\) into the first equation to solve for \(y\)

Substitute \(x = 5\) into \(3x+5y = 5\):
\(3\times5+5y = 5\)
\(15 + 5y=5\)
Subtract \(15\) from both sides: \(5y=5 - 15=- 10\)
Divide both sides by \(5\): \(y=\frac{-10}{5}=-2\)

Answer:

\(x = 5\), \(y=-2\)