Question

SOLVE BY SUBSTITUTION:

3x-2y=14
y=5x
solve by substitution
x-2y=-2
y=2x+4
solve by elimination
x+2y=-7
x-5y=7
PLEASE HELP WORTH 10 POINTS! AKA SHOW WORK:)

Answer 1

1)


`3x-2y=14\\ \\ y=5x`

We know y's value. Let's plug it in the equation.


`y=5x\\ \\ 3x-2\cdot (5x)=14\\ \\ 3x-10x=14\\ \\ -7x=14`

Divide both sides by -7.


`x=-2`

Now we have x's value. Let's plug it in the equation to find y.


`x=-2\\ \\ y=5x\\ \\ y=5\cdot -2\\ \\ y=-10`

Solution,

(-2, -10)

2)

`x-2y=-2\\ \\ y=2x+4`

Again we have y's value. Let's plug and solve.


`y=2x+4\\ \\ x-2\cdot (2x+4)=-2\\ \\ x-(2\cdot 2x+2\cdot 4)=-2\\ \\ x-4x-8=-2\\ \\ -3x-8=-2\\ \\ -3x=-2+8\\ \\ -3x=6\\ \\ x=\frac { 6 }{ -3 } \\ \\ x=-2`

Now we have x's value let's solve for y.


`x=-2\\ \\ y=2x+4\\ \\ y=2\cdot (-2)+4\\ \\ y=-4+4\\ \\ y=0`

Solution,

(-2, 0)

3)


`x+2y=-7\\ \\ x-5y=7`

Let's first multiply the first equation by -1


`-1\cdot (x+2y)=-1\cdot -7\\ \\ -x-2y=7`

Then let's add these new equation and the second equation.


`-1\cdot (x+2y)=-1\cdot -7\\ \\ -x-2y=7\\ \\ x-5y=7\\ \\ (-x-2y)+(x-5y)=7+7\\ \\ -x+x-2y-5y=14\\ \\ -7y=14\\ \\ y=\frac { 14 }{ -7 } \\ \\ y=-2`

Now we have y's value let's plug it and solve for x.


`y=-2\\ \\ x+2y=-7\\ \\ x+2\cdot (-2)=-7\\ \\ x-4=-7\\ \\ x=-7+4\\ \\ x=-3`

Solution,

(-3, -2)

Answer 2

1)
3x-2y=14
y=5x

So we plug in y=5x into 3x-2y=14

We get:

3x-2(5x)=14
3x -10x=14
-7x=14
x=-2

So we found x, now we need to find y. We can simply plug in x into the equation and get y.

y=5x
y=5(-2)
y=-10

So your answer will be (-2,-10).

2)
x-2y= -2
y= 2x+4

Once again plug in y=2x+4 into x-2y=-2

x-2(2x+4) = -2
x-4x-8=-2
-3x-8=-2
-3x = 6
x= -2

Now we plug back in x and solve for y :)

y=2x+4
y=2(-2)+4
y=-4+4
y=0

So our solution would be (-2,0).

3)
x+2y=-7
x-5y=7

Multiply the second equation by -1

-x+5y=-7

Now add that equation with the other one:

x+2y=-7
+
-x+5y=-7
-----------------
7y=-14
y=-2

Now plug in y=-2 and solve for x

x+2y=-7
x+2(-2)=-7
x+(-4)=-7
x-4=-7
x=-3

So your solution would be (-3,-2).