Question

4. Which statement explains why 13x - 13y = -26 shares a solution with thissystem of equations: *102 - 3y = 29-3x + 10y = 55Because 13x - 13y = -26 is the product of the two equations in the system ofequations, it the must share a solution with the system of equations.The three equations all have the same slope but different y-intercepts. Equations withthe same slope but different y-intercepts always share a solution.Because 10x - 3y is equal to 29, I can add 10x - 3y to the left side of -3x+10y = 55 andadd 29 to the right side of the same equation. Adding equivalent expressions to eachside of an equation does not change the solution to the equation.Because -3x+10y is equal to 55, I can subtract-3x+10y from the left side of 10x - 3y= 29 and subtract 55 from its right side. Subtracting equivalent expressions from eachside of an equation does not change the solution to the equation.

Answer 1

To evaluate which option is the correct one, we have to try it one by one.

• First option

To know the solution of a system of equations, we can do it by graphing, substitution, or addition. Additionally, the multiplication of the equations does not equal the equation given in the question. Then this is not the correct option.

• Second option

To evaluate this option it is easier to have the equations in the form:

$y=mx+b$

where m equals the slope and b equal the y-intercept.

The equation:

$13x-13y=-26$

can be changed in the form:

$y=x+\frac{26}{13}$

In this case m = 1 and b = 26/13

The equation:

$10x-3y=29$

can be changed in the form:

$y=\frac{10}{3}x-\frac{29}{3}$

In this case m =10/3 and b = -29/3.

There is no need to evaluate the third equation as the slopes between these two are different, then this is NOT the correct option either.

• Third option

Adding (10x-3y) and 29

$-3x+10y+(10x-3y)=55+29$

Simplifying:

$7x+7y=84$

As this is not the equation then it is not an option either.

Fourth option

Substracting (-3x+10y) and 55

$10x-3y-(-3x+10y)=29-55$

Simplifying:

$10x-3y+3x-10y=-26$$13x-13y=-26$

This is our equation.

Answer: Fourth option