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2 years ago

Solve the following system by the substitution method.1/4x+2/3y=-17/43x-y=3

1 answer:

6 0

3x - y = 3.....3x - 3 = y

1/4x + 2/3(3x - 3) = -17/4
1/4x + 2x - 2 = -17/4 ...multiply everything by 4
x + 8x - 8 = -17
9x = -17 + 8
9x = - 9
x = -1

3x - y = 3
3(-1) - y = 3
-3 - y = 3
-3 - 3 = y
-6 = y

solution is (-1,-6)

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If u = 2i - j; v= -5i + 4j and w = j find 4u (v -w).

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Answer:

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Explanation:

Given

u = 2i - j; v= -5i + 4j and w = j

Required

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Which matrix equation represents the system of equations?<br><br> {-x+ 2y = 0 <br> y= -2

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We are given a system of equations,

$\begin{cases}-x+2y=0\\y=-2\\ \end{cases}$

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

$\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}$

The matrix will then be applied to the vector (lower dimensions on top),

$\begin{bmatrix}x\\y\\ \end{bmatrix}$

And the result vector will be whats on the other side of equals sign,

$\begin{bmatrix}0\\-2\\ \end{bmatrix}$

So to put everything together,

$\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}$

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