r subs titut lon. -3x-2y=5 -2x+1=y

To solve the system of equations using substitution, we first need to express one variable in terms of the other using one of the equations. Let's use the second equation:<br /><br />\[<br />-2x + 1 = y<br />\]<br /><br />Now that we have \( y \) expressed in terms of \( x \), we can substitute this expression for \( y \) into the first equation:<br /><br />\[<br />-3x - 2(-2x + 1) = 5<br />\]<br /><br />Simplify the equation:<br /><br />\[<br />-3x + 4x - 2 = 5<br />\]<br /><br />Combine like terms:<br /><br />\[<br />x - 2 = 5<br />\]<br /><br />Add 2 to both sides to solve for \( x \):<br /><br />\[<br />x = 7<br />\]<br /><br />Now that we have the value of \( x \), substitute it back into the expression for \( y \):<br /><br />\[<br />y = -2(7) + 1<br />\]<br /><br />Calculate the value of \( y \):<br /><br />\[<br />y = -14 + 1 = -13<br />\]<br /><br />Thus, the solution to the system of equations is:<br /><br />\[<br />x = 7, \quad y = -13<br />\]