Question 357156
{{{y=-2x+7}}} Start with the first equation.



{{{x^2-4x=-2x+7}}} Plug in {{{y=x^2-4x}}}



{{{x^2-4x+2x-7=0}}} Get every term to the left side.



{{{x^2-2x-7=0}}} Combine like terms.



Notice that the quadratic {{{x^2-2x-7}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-2}}}, and {{{C=-7}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-2) +- sqrt( (-2)^2-4(1)(-7) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-2}}}, and {{{C=-7}}}



{{{x = (2 +- sqrt( (-2)^2-4(1)(-7) ))/(2(1))}}} Negate {{{-2}}} to get {{{2}}}. 



{{{x = (2 +- sqrt( 4-4(1)(-7) ))/(2(1))}}} Square {{{-2}}} to get {{{4}}}. 



{{{x = (2 +- sqrt( 4--28 ))/(2(1))}}} Multiply {{{4(1)(-7)}}} to get {{{-28}}}



{{{x = (2 +- sqrt( 4+28 ))/(2(1))}}} Rewrite {{{sqrt(4--28)}}} as {{{sqrt(4+28)}}}



{{{x = (2 +- sqrt( 32 ))/(2(1))}}} Add {{{4}}} to {{{28}}} to get {{{32}}}



{{{x = (2 +- sqrt( 32 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (2 +- 4*sqrt(2))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (2)/(2) +- (4*sqrt(2))/(2)}}} Break up the fraction.  



{{{x = 1 +- 2*sqrt(2)}}} Reduce.  



{{{x = 1+2*sqrt(2)}}} or {{{x = 1-2*sqrt(2)}}} Break up the expression.  



So the solutions are {{{x = 1+2*sqrt(2)}}} or {{{x = 1-2*sqrt(2)}}}



Now let's find the corresponding y values.



Let's find the value of y when {{{x = 1+2*sqrt(2)}}}



{{{y=-2x+7}}} Start with the first equation.



{{{y=-2(1+2*sqrt(2))+7}}} Plug in {{{x = 1+2*sqrt(2)}}}



{{{y=-2-4*sqrt(2)+7}}} Distribute.



{{{y=5-4*sqrt(2)}}} Combine like terms.



So when {{{x = 1+2*sqrt(2)}}}, {{{y=5-4*sqrt(2)}}} which gives us the ordered pair *[Tex \LARGE \left(1+2\sqrt{2},5-4\sqrt{2}\right)]



Now let's find the value of y when {{{x = 1-2*sqrt(2)}}}



{{{y=-2x+7}}} Start with the first equation.



{{{y=-2(1-2*sqrt(2))+7}}} Plug in {{{x = 1-2*sqrt(2)}}}



{{{y=-2+4*sqrt(2)+7}}} Distribute.



{{{y=5+4*sqrt(2)}}} Combine like terms.



So when {{{x = 1-2*sqrt(2)}}}, {{{y=5+4*sqrt(2)}}} which gives us the ordered pair *[Tex \LARGE \left(1-2\sqrt{2},5+4\sqrt{2}\right)]