Solve the system by the method of substitution.Check your solution(s)graphically. $$\left\{ \begin{aligned}
x - y & = - 3 \
x ^ { 2 } - y & = 3
\end{aligned} \right.$$
A)(3,6), (1,-2)
B)(5,5), (1,-2)
C)(6,3), (-3,6)
D)(3,6), (-2,1)
E)(5,5), (-2,1)

Question

Solve the system by the method of substitution.Check your solution(s)graphically.​ $$\left\{ \begin{aligned}
x - y & = - 3 \
x ^ { 2 } - y & = 3
\end{aligned} \right.$$ ​​  ​
A)(3,6), (1,-2) 
B)(5,5), (1,-2) 
C)(6,3), (-3,6) 
D)(3,6), (-2,1) 
E)(5,5), (-2,1)

Quizplus · Accepted Answer

To solve by substitution, we solve one equation for one of the variables, and then substitute that expression into the other equation. 
From the first equation, we can get x in terms of y: 
$x = y+3$

Substituting this expression for x into the second equation gives: 
$(y+3)+y=9$
$2y+3=9$
$2y=6$
$y=3$

Substituting y=3 back into the first equation gives: 
$x=3+3$
$x=6$

Therefore, the solution is (6,3). 
To check this, we can graph the two equations and see where they intersect:

![graph](https://i.imgur.com/kKjJFkH.png)

We see that the point (6,3) is the intersection point of the two lines, confirming our solution.

(Note: the other two points listed in the answer choices are not solutions to the system of equations.)

Solve the System by the Method of Substitution {x−y=−3x2−y=3\left\{ \begin{aligned}x - y & = - 3 \\x ^ { 2 } - y & = 3\end{aligned} \right.{x−yx2−y​=−3=3​

Solve the System by the Method of Substitution $\left\{ \begin{aligned}x - y & = - 3 \\x ^ { 2 } - y & = 3\end{aligned} \right.$