Verified Answer :
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, \(\frac{5}{3}\)).
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 \(x=-2,\ {\text{is} \left({ - 2,\dfrac{5}{3}}\right).\)
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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.