Question 198241
{{{2y-x=-10}}} Start with the second equation.



{{{2(x-7)-x=-10}}}  Plug in {{{y=x-7}}} into the first equation. In other words, replace each {{{y}}} with {{{x-7}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{2x-14-x=-10}}} Distribute



{{{x-14=-10}}} Combine like terms on the left side



{{{x=-10+14}}}Add 14 to both sides



{{{x=4}}} Combine like terms on the right side




Now that we know that {{{x=4}}}, we can plug this into {{{y=x-7}}} to find {{{y}}}



{{{y=x-7}}} Start with the first equation.



{{{y=(4)-7}}} Plug in {{{x=4}}}



{{{y=-3}}} Subtract



So our answer is {{{x=4}}} and {{{y=-3}}} which also looks like *[Tex \LARGE \left(4,-3\right)]



Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(4,-3\right)]. So this verifies our answer.


{{{ drawing(500, 500, -10, 10, -10, 10,
 grid(1),
 graph( 500, 500, -10, 10, -10, 10,x-7, (-10+x)/2)

)}}}


Graph of  {{{y=x-7}}} (red) and {{{2y-x=-10}}} (green)