3. What is the x-coordinate of the solution of the following system? ) 3x+10y=1 x+2y=-1

To find the \( x \)-coordinate of the solution to the system of equations:<br /><br />\[<br />\begin{cases}<br />3x + 10y = 1 \\<br />x + 2y = -1<br />\end{cases}<br />\]<br /><br />we can use the method of substitution or elimination. Here, we will use the elimination method.<br /><br />First, let's multiply the second equation by 3 to align the coefficients of \( x \):<br /><br />\[<br />3(x + 2y) = 3(-1)<br />\]<br /><br />This simplifies to:<br /><br />\[<br />3x + 6y = -3<br />\]<br /><br />Now, we have the following system of equations:<br /><br />\[<br />\begin{cases}<br />3x + 10y = 1 \\<br />3x + 6y = -3<br />\end{cases}<br />\]<br /><br />Next, subtract the second equation from the first equation to eliminate \( x \):<br /><br />\[<br />(3x + 10y) - (3x + 6y) = 1 - (-3)<br />\]<br /><br />Simplifying this, we get:<br /><br />\[<br />4y = 4<br />\]<br /><br />Solving for \( y \):<br /><br />\[<br />y = 1<br />\]<br /><br />Now that we have \( y = 1 \), substitute this value back into the second original equation to solve for \( x \):<br /><br />\[<br />x + 2(1) = -1<br />\]<br /><br />Simplify and solve for \( x \):<br /><br />\[<br />x + 2 = -1 \\<br />x = -1 - 2 \\<br />x = -3<br />\]<br /><br />Therefore, the \( x \)-coordinate of the solution is:<br /><br />\[<br />\boxed{-3}<br />\]