Solve the system of equations using the substitution method.

Mathematics

2 answers:

Kitty [74]2 years ago

8 0

Answer:

Step-by-step explanation:

x = -5/8 and y = -7/4

x = -0.625 and y = -2.25

alexandr1967 [171]2 years ago

5 0

Answer:

x = -0.625

y = - 1.75

Step-by-step explanation:

y = 2x - 1/2 ------------(I)

2x - 3y = 4 ---------(II)

Substitute y =2x - 1/2 in (II)

$2x - 3*(2x - \dfrac{1}{2})=4\\\\\\2x - 6x + \dfrac{3}{2}=4\\\\-4x = 4-\dfrac{3}{2} = \dfrac{8}{4}- \dfrac{3}{2}\\\\-4x = \dfrac{5}{2}\\\\x = \dfrac{5}{2}* \dfrac{1}{-4}\\\\x= \dfrac{-5}{8}\\\\x= -0.625$

Plugin x = -0.625 in equation (I)

$y = 2*(-0.625) - 0.5\\\\y = -1.25 - 0.5\\\\y = -1.75$

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<h3><u>Explanation</u></h3>

Modulus Function

$y = a |x - h| + k$

The structure or equation is similar to a quadratic function.

The value of a determines the slope of graph.

Tthe value of h determines the horizontal shift of graph.

The value of k determines the vertical shift of the graph.

From the given equation,

$f(x) = |x - 2| - 7$

We can say that the graph shifts to the right 2 units and shifts down 7 units. Hence the vertex would be at x = 2 and y = -7. It can be written in coordinate form as (2,-7).

<h3><u>Answer</u></h3>

<u> $\large{(2,-7)}$ </u>