Question

solve the system of equations $-5x + 3y = 0$ and $7x - 4y = 2$ by combining the equations.
$\square\\ (-5x +3y = 0)$
$\square\\ (7x \\ \\ -4y = 2)$
$\

$$\begin{array}{r}-5x +3y = 0\\\\7x -4y = 2\\\\\\hline\\square\\ x + \\square\\ y= \\square\\end{array}$$

$

Explanation:

Step1: Add the x-terms

To combine the equations, we first add the coefficients of \(x\) from both equations. The coefficient of \(x\) in the first equation is \(-5\) and in the second is \(7\). So, \(-5x + 7x = (-5 + 7)x = 2x\).

Step2: Add the y-terms

Next, we add the coefficients of \(y\) from both equations. The coefficient of \(y\) in the first equation is \(3\) and in the second is \(-4\). So, \(3y + (-4y) = (3 - 4)y = -y\).

Step3: Add the constant terms

Finally, we add the constant terms from both equations. The constant term in the first equation is \(0\) and in the second is \(2\). So, \(0 + 2 = 2\).

Putting it all together, when we combine the two equations by adding them, we get \(2x - y = 2\).

Answer:

\(2x - y = 2\) (So the blanks are filled with 2, -1, and 2 respectively)