Answer :
let x be the amount of panels that plant A produced and y the amount of panels that plant B produced. First we are told that plant A produced 2000 fewer panels tan plant B. This means that if we subtract 2000 from the amount that plant B produced, we would get the amount that plant A produced. This translates to the equation
[tex]y\text{ -2000=x}[/tex]which is equivalent to the equation
[tex]y\text{ -x=2000}[/tex]next, we will calculate the amount of defective panels per plant and then add them up. THis final quantity should be 660. We are told that 2% of plant A's production is defective and that 5% of plant B's production is defective. Recall that to calculate the x% of a number, we simply mulitply the number by x and divide it by 100. So we have that 2% of plant A's production would be
[tex]\frac{2}{100}x[/tex]and the 5% of plant B's production would be
[tex]\frac{5}{100}y[/tex]if we add this quantities, we get the equation
[tex]\frac{2}{100}x+\frac{5}{100}y=660[/tex]If we multiply both sides by 100, we get the equivalent equation
[tex]2x+5y=66000[/tex]NOw, we want to solve this system of linear equations to find the values of x and y. MOre especifically, we want the value of y. Let us take the first equation, multiply it by 2 and then add it to the second equation, so we get
[tex]2x+5y+2\cdot(y\text{ -x)=66000+2}\cdot2000=70000[/tex]on the left we get
[tex]2x+5y+2y\text{ -2x=7y=664000}[/tex]so, if we divide both sides by 7, we get
[tex]y=\frac{70000}{7}=10000[/tex]so plant B produced 10000 panels