Question

Which graph represent the solution to the given systems y=-x +4 y=1/3x + 8

Answer 1

Use substitution

-x + 4 = 1/3x + 8
4 = 4/3x + 8
-4 = 4/3x
x = -4 * 3/4
x = -3

Then plug x into one of the original equations. In this case y = -x + 4 is the easiest.

y = -(-3) + 4
y = 7

Answer 2

The solution of the given systems $y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8$ is $\boxed{\left( { - 3,7} \right)}$. Option (a) is correct.

Further explanation:

Given:

The system of equations is $y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8.$

The options are as follows,

(a). $\left( { - 3,7} \right)$

(b). $\left( {0,8} \right)$

(c). $\left( { 3,7} \right)$

(d). $\left( {0,4} \right)$

Explanation:

The given system of equations is $y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8.$

Equate the two equations to obtain the solution of the system of equation.

$\begin{aligned}- x + 4 &= \frac{1}{3}x + 8\\- x - \frac{1}{3}x & 8 - 4\\\frac{{ - 3x - x}}{3} &= 4\\- 4x &= 12\\x&= - 3\\\end{aligned}$

The value of y can be obtained as follows,

$\begin{aligned}y &= - \left( { - 3} \right) + 4\\&= 3 + 4\\&= 7\\\end{aligned}$

The solution of the given systems $y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8$ is $\boxed{\left( { - 3,7} \right)}$. Option (a) is correct.

Learn more:

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: system of equations, numbers,slope, slope intercept, equation, y-intercept, graph, representation, origin.