Question 46819
Solve the simultaneous equations (aka: System of equations):
1) {{{y = x^2+2x+9}}}
2) {{{7x+y = 19}}}

You can solve this system of equations (aka: Simultaneous equations) by the "susbtitution" method.
Substitute equation 1) into equation 2) for y and solve for x.

{{{7x + (x^2+2x+9) = 19}}} Simplify and solve for x.
{{{x^2+9x+9 = 19}}} Subtract 19 from both sides of the equation.
{{{x^2+9x-10 = 0}}} Solve this quadratic equation by factoring.
{{{(x-1)(x+10) = 0}}} Apply the zero products principle.
{{{x-1 = 0}}} and/or {{{x+10 = 0}}}
If {{{x-1 = 0}}} then {{{x = 1}}}
If {{{x+10 = 0}}} then {{{x = -10}}}

Now, to find the value of y, substitute the values of x, one-at-a-time into either of the two original equations and solve for y. Let's take the first equation {{{y = x^2+2x+9}}} and substitute x = 1 then solve for y.
{{{y = 1^2+2(1)+9}}}
{{{y = 12}}}

So one of the solutions is: x = 1, y = 12 or (1,12)

Just as a check, you can see that, had we substituted x = 1 into the second equation, we would have obtained the same result.

{{{7(1) + y = 19}}} Subtact 7 from both sides.
{{{y = 12}}} Same as before.

Now to get the second solution, substitute x = -10 into the first equation and solve for y.
{{{y = (-10)^2+2(-10)+9}}}
{{{y = 100-20+9}}}
{{{y = 89}}}

Now let's try using the second equation.

{{{7(-10) + y = 19}}} 
{{{-70 + y = 19}}} Add 70 to both sides.
{{{y = 89}}} Same as before.

The second solution is: x = -10, y = 89 or (-10, 89}