Question

determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
$2x + y = 7$
$-2x + 2y = -5$
answer attempt 1 out of 3
\\(\circ\\) one solution
\\(\circ\\) infinitely many solutions
\\(\circ\\) no solutions
submit answer

Explanation:

Step1: Add the two equations

$$(2x + y) + (-2x + 2y) = 7 + (-5)$$
Simplify:
$$3y = 2$$

Step2: Solve for $y$

$$y = \frac{2}{3}$$

Step3: Substitute $y$ into first equation

$$2x + \frac{2}{3} = 7$$

Step4: Solve for $x$

$$2x = 7 - \frac{2}{3} = \frac{21}{3} - \frac{2}{3} = \frac{19}{3}$$
$$x = \frac{19}{6}$$

Answer:

One Solution