How do you solve the system of equations $- 7 x + 2 y = 7$ $-7x + 2y = 7$ and $y = 3 x$ $y = 3x$ ?

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Answer 1 · 2017-03-27T16:07:24

See the entire solution process below:

Step 1) Because the second equation is already solved for $y$ $y$ , substitute $3 x$ $3x$ for $y$ $y$ in the first equation and solve for $x$ $x$ :

$- 7 x + 2 y = 7$ $-7x + 2y = 7$ becomes:

$- 7 x + 2 (3 x) = 7$ $-7x + 2(3x) = 7$

$- 7 x + 6 x = 7$ $-7x + 6x = 7$

$(- 7 + 6) x = 7$ $(-7 + 6)x = 7$

$- 1 x = 7$ $-1x = 7$

$- 1 \times - 1 x = - 1 \times 7$ $color(red)(-1) xx -1x = color(red)(-1) xx 7$

$1 x = - 7$ $1x = -7$

$x = - 7$ $x = -7$

Step 2) Substitute $- 7$ $-7$ for $x$ $x$ in the second problem and calculate $y$ $y$ :

$y = 3 x$ $y = 3x$ becomes:

$y = 3 \times - 7$ $y = 3 xx -7$

$y = - 21$ $y = -21$

The solution is: $x = - 7$ $x = -7$ and $y = - 21$ $y = -21$ or $(- 7, - 21)$ $(-7, -21)$

How do you solve the system of equations −7x+2y=7-7x + 2y = 7 and y=3xy = 3x?