Question

Sole by substitution. -3x+2y=16 X-2y=-12

Answer 1

Answer:

For the given equations the values of x and y by using substitution method are  $x=1$  and $y=\frac{13}{2}$

Step-by-step explanation:

Given system of equations are

$-3x+2y=16\hfill (1)$

$x-2y=-12\hfill (2)$

Solve the given equations by substitution method:

Now (2) implies

$x-2y=-12$

$x=-12+2y\hfill (3)$

Now substitute the x value in equation (1)

$-3x+2y=16$

$-3(-12+2y)+2y=16$

$36-6y+2y=16$

$36-4y=16$

$-4y=16-36$

$y=-(\frac{-26}{4})$

$y=\frac{26}{4}$

Therefore  $y=\frac{13}{2}$

Now substitute the y value in equation (3)

$x=-12+2y$

$x=-12+2\times \frac{13}{2}$

$x=-12+13$

$x=1$

Therefore $x=1$  and $y=\frac{13}{2}$

Answer 2

Answer: (-2,5)

Step 1: Rewrite equations

-3x+2y=16

x-2y=-12

Step 2: Changing the second equation

With substitution, you have to already have the equation to solve for the specific variable (ex: x=y+1;y=x+1). Since the equation doesn’t give us one, we can flip the second equation to give us this.

Let’s add 2y on both sides.

x-2y=-12
+2y +2y
_________
x=2y-12

Now we have the equation to solve for x!

Step 3: Substituting

Now we need to substitute x into the first equation. Let’s do this now.

-3(2y-12)+2y=16

Step 4: Solving for y

-3(2y-12)+2y=16

*distribute*

-6y+36+2y=16

*combine like terms*

-4y+36=16

*subtract 36 on both sides*

-4y=-20

*divide both numbers by -4*

y=5

This is y! Now we need to solve for x.

Step 5: Solving for x

To find x, let’s just substitute y into the equation and solve

x=2y-12

x=2(5)-12

x=10-12

x=-2

Step 6: Ordered pair

(X,y) —> (-2,5)


This is your answer! Hope this helps comment below for more questions :)