Respuesta :
Answer:
solution (-2, [tex]\frac{5}{3}[/tex]).
Step-by-step explanation:
Given : y = [tex]\frac{2x}{3}[/tex] + 3 and x = –2.
To find : What is the solution to the system of equations.
Solution : We have given that y = [tex]\frac{2x}{3}[/tex]+ 3 ------equation (1)
and x = –2. ------equation (2)
On plugging the x = -2 in equation (1)
y = [tex]\frac{2(-2)}{3}[/tex] + 3
y = [tex]\frac{-4}{3}[/tex] + 3 .
On simplification we get ,
y = [tex]\frac{5}{3}[/tex].
Therefore, solution (-2, [tex]\frac{5}{3}[/tex]).
The solution of the system of equation [tex]y=\dfrac{2}{3}x + 3[/tex] and [tex]x=-2, \text {is} \left( { - 2,\dfrac{5}{3}}\right).[/tex]
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}}\right)[/tex] and [tex]\left( {{x_2},{y_2}}\right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The system of equations are [tex]y =\dfrac{2}{3}x + 3[/tex] and x=-2.
Explanation:
The given system of equations are [tex]y = \dfrac{2}{3}x + 3[/tex] and x=-2.
Solve the two equations to obtain the solution.
Substitute x = - 2 in equation [tex]y=\dfrac{2}{3}x + 3[/tex] to obtain the value of y.
[tex]\begin{aligned}y&= \frac{2}{3}\left( { - 2} \right)+ 3\\&= \frac{{ - 4}}{3} + 3\\&= \frac{{ - 4 + 9}}{3}\\&=\frac{5}{3}\\\end{aligned}[/tex]
The value of y is [tex]\dfrac{5}{3}.[/tex]
The solution of the system of equation [tex]y =\dfrac{2}{3}x + 3[/tex] and [tex]x=-2,\ {\text{is} \left({ - 2,\dfrac{5}{3}}\right).[/tex]
Learn more:
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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.
