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When Ron-Jon multiplies the second equation by $-5,$ he must multiply both sides for the equality to hold. In his solution Ron-Jon only multiplied the left-hand side but forgot the right-hand side. $x−3y=-11⇔ -5x+15y=-11$
When the second equation is multiplied by $-5$ it should instead look like this
Ron-Jon's system then looks like this.
${-5x+14y=7-5x+15y=55 $
Adding the equations will lead to the $x$-terms eliminating each other.
$+ -5x+14y-5x+15y19y === 75562 $
The correct value of $y$ is then found by solving the resulting equation.
$19y=62⇔y=1962 $

$x−3y=-11$

MultEqn$LHS⋅(-5)=RHS⋅(-5)$

$-5(x−3y)=-5(-11)$

DistrDistribute $(-5)$

$-5x+15y=-5(-11)$

MultNegNegOnePar$-a(-b)=a⋅b$

$-5x+15y=55$