Which of the following equations could be the result of multiplication and addition to eliminate a variable in the system of equations? 19y=22 A 19x=24 11 y=22

To determine which equation could be the result of multiplying and adding to eliminate a variable in the system of equations, we need to analyze the given equations.<br /><br />Given equations:<br />1. $19y = 22$<br />2. $19x = 24$<br />3. $11y = 22$<br /><br />Let's analyze each equation:<br /><br />1. $19y = 22$: This equation represents a linear equation with one variable, y.<br />2. $19x = 24$: This equation represents a linear equation with one variable, x.<br />3. $11y = 22$: This equation represents a linear equation with one variable, y.<br /><br />To eliminate a variable in the system of equations, we need to multiply and add the equations in such a way that one of the variables cancels out.<br /><br />In this case, we can multiply the first equation ($19y = 22$) by 11 and the third equation ($11y = 22$) by 19. This will allow us to eliminate the variable y.<br /><br />Multiplying the first equation by 11:<br />$19y \times 11 = 22 \times 11$<br />$209y = 242$<br /><br />Multiplying the third equation by 19:<br />$11y \times 19 = 22 \times 19$<br />$209y = 418$<br /><br />Now, we can add these two equations to eliminate the variable y:<br />$209y + 209y = 242 + 418$<br />$418y = 660$<br /><br />Simplifying the equation:<br />$y = \frac{660}{418}$<br />$y = \frac{330}{209}$<br /><br />Therefore, the equation that could be the result of multiplying and adding to eliminate a variable in the system of equations is $209y = 660$.<br /><br />So, the correct answer is: $209y = 660$.