Question

What is the solution to the system of equations? y = 2/3x + 3 x = –2

Answer 1

Answer:

solution (-2,  $\frac{5}{3}$).

Step-by-step explanation:

Given : y = $\frac{2x}{3}$ + 3  and x = –2.

To find : What is the solution to the system of equations.

Solution : We have given that y = $\frac{2x}{3}$+ 3 ------equation (1)

and                                            x = –2.   ------equation (2)

On plugging the x = -2 in equation (1)

y = $\frac{2(-2)}{3}$ + 3

y = $\frac{-4}{3}$ + 3 .

On simplification we get ,

y = $\frac{5}{3}$.

Therefore, solution (-2,  $\frac{5}{3}$).

Answer 2

The solution of the system of equation $y=\dfrac{2}{3}x + 3$ and $x=-2, \text {is} \left( { - 2,\dfrac{5}{3}}\right).$

Further explanation:

The linear equation with slope m and intercept c is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}}\right)$ and $\left( {{x_2},{y_2}}\right)$ can be expressed as,

$\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

Given:

The system of equations are $y =\dfrac{2}{3}x + 3$ and x=-2.

Explanation:

The given system of equations are $y = \dfrac{2}{3}x + 3$ and x=-2.

Solve the two equations to obtain the solution.

Substitute x =  - 2 in equation $y=\dfrac{2}{3}x + 3$ to obtain the value of y.

$\begin{aligned}y&= \frac{2}{3}\left( { - 2} \right)+ 3\\&= \frac{{ - 4}}{3} + 3\\&= \frac{{ - 4 + 9}}{3}\\&=\frac{5}{3}\\\end{aligned}$

The value of y is $\dfrac{5}{3}.$

The solution of the system of equation $y =\dfrac{2}{3}x + 3$ and $x=-2,\ {\text{is} \left({ - 2,\dfrac{5}{3}}\right).$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequalities

Keywords: numbers, slope, slope intercept, inequality, equation, linear equation, shaded region, y-intercept, graph, representation, origin, perpendicular, x-intercept 6, x-intercept.