7x-3y=4 2x-4y=1 The solution to the system of equations is __ (3/22,-7/22) (13/22,1/22) (13/34,-15/34)

To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.<br /><br />First, we can multiply the second equation by 2 to make the coefficients of x in both equations equal:<br /><br />$4x - 8y = 2$<br /><br />Now we have the system of equations:<br /><br />$7x - 3y = 4$<br />$4x - 8y = 2$<br /><br />Next, we can multiply the first equation by 4 and the second equation by 7 to make the coefficients of x in both equations equal:<br /><br />$28x - 12y = 16$<br />$28x - 56y = 14$<br /><br />Now we can subtract the second equation from the first equation to eliminate x:<br /><br />$28x - 12y - (28x - 56y) = 16 - 14$<br /><br />Simplifying, we get:<br /><br />$44y = 2$<br /><br />Dividing both sides by 44, we get:<br /><br />$y = \frac{1}{22}$<br /><br />Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:<br /><br />$7x - 3y = 4$<br /><br />Substituting $y = \frac{1}{22}$, we get:<br /><br />$7x - 3(\frac{1}{22}) = 4$<br /><br />Simplifying, we get:<br /><br />$7x - \frac{3}{22} = 4$<br /><br />Adding $\frac{3}{22}$ to both sides, we get:<br /><br />$7x = 4 + \frac{3}{22}$<br /><br />Combining the terms on the right side, we get:<br /><br />$7x = \frac{88}{22} + \frac{3}{22} = \frac{91}{22}$<br /><br />Dividing both sides by 7, we get:<br /><br />$x = \frac{91}{22 \cdot 7} = \frac{13}{22}$<br /><br />Therefore, the solution to the system of equations is $(\frac{13}{22}, \frac{1}{22})$.<br /><br />So the correct answer is $(13/22, 1/22)$.