Question #17602

3 Answers
Jan 4, 2018

Use the elimination or substitution methods

Explanation:

Here I would use the elimination method and get rid of the y variable. The first equation can be multiplied by 3 to make the equation -9x-6y=-15

Then add the two equations together to get rid of the y variable and solve for the x
-9x-6y=-15
ul(+ 7x+6y=+1 larr" Add")
-2x+color(white)(".")0=-14

=>color(red)(x=7)

Plug in for y

7( color(red)(7) )+6y=1

49+6y=1

6y=-48

y=-8

Double check by plugging in both solutions
The answer is (7, -8)

Jan 4, 2018

x=7
y=-8

Explanation:

{(-3x-2y=-5),(7x+6y=1):}

Let's procede finding the x of the second equation:
{ (-3x-2y=-5),(7x=-6y+1):}

{(-3x-2y=-5),(x=-\frac{6}{7}y+\frac{1}{7}):}

Now we can substitute the x that we found in the first equation:
{(-3(-\frac{6}{7}y+\frac{1}{7})-2y=-5),(x=-\frac{6}{7}y+\frac{1}{7}):}

{(\frac{18}{7}y-\frac{3}{7}-2y=-5),(x=-\frac{6}{7}y+\frac{1}{7}):}

{(\frac{18}{7}y-2y=-5+\frac{3}{7}),(x=-\frac{6}{7}y+\frac{1}{7}):}

{(\frac{18-14}{\cancel{7}}y=\frac{3-35}{\cancel{7}}), (x=-\frac{6}{7}y+\frac{1}{7}):}

{(4y=-32),(x=-\frac{6}{7}y+\frac{1}{7}):}

{(y=-8),(x=-\frac{6}{7}y+\frac{1}{7}):}

Now let's substitute y=-8 in the second equation:
{(y=-8),(x=-\frac{6}{7}(-8)+\frac{1}{7}):}

{(y=-8),(x=\frac{48}{7}+\frac{1}{7}):}

{(y=-8),(x=\frac{49}{7}=7):}

Final result:
x=7
y=-8

Jan 4, 2018

Have a look at https://socratic.org/help/symbols Note the hash symbols at the beginning and end of the entered text.

x=7 and y=-8

Explanation:

Given:
color(green)(-3x-2y=-5" "....................Equation(1))
color(green)(+7x+6y=+1" "....................Equation(2))

[7xxEqn(1)]+[3xxEqn(2)]
color(white)("dddddddddd") darr

color(green)(-21x-14y=-35" "....Equation(1_a))
color(green)(ul(+21x+18y=+color(white)(5)3)........Equation(2_a))
color(green)(color(white)("dd")0color(white)("d.")+color(white)("d")4y=-32)

color(green)( y=-8 )
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I choose Eqn(2)
Substitute for color(red)(y) in Eqn(2) giving:

color(green)(+7x+6color(red)(y)=+1color(white)("ddd")->color(white)("ddd")7x+[6color(red)(xx(-8))]=1)

color(white)("ddddddddddddddd.d")color(green)(->color(white)("ddd")7x-color(white)("ddd")48color(white)("dddd")=1)

color(white)("ddddddddddddddd.d")color(green)(->color(white)("ddddddddddddd.d")7x=49)

color(green)(color(white)("ddddddddddddddddd")->color(white)("ddddddddddddddd") x=49/7=7 )