Question

Solve the system by using elimination or elimination with multiplication. One point for the steps and one point for the correct solution.

3x + 4y = -2 and 2x - 3y = 10

Answer 1

Lets do the substitution method...

Solve the second equation for (lets do 'x')

Add 3y to both sides

2x - 3y = 10
+3y +3y
----------------
2x = 3y + 10 <---now divide everything by 2 to solve for 'x'
------------
2 2 2

x = (3/2)y + 5

Now that we know what 'x' equals...we substitute that into the first equation we have for 'x'

3x + 4y = -2

After substituting that in...we have

\[\large 3(\frac{3}{2}y + 5) + 4y = -2 \]

Simpify a bit...

\[\large \frac{9}{2}y + 15 + 4y = -2\]

Combine like terms...

\[\large \frac{17y}{2} + 15 = -2\]

Subtract 15 from both sides...

\[\large \frac{17y}{2} = -17\]

Multiply both sides by 2

\[\large 17y = -34\]

Divide both sides by 17

\[\large y = -2\]

Now that we know y = -2 we can use that to solve for 'x' go back to our first original equation...

\[\large 3x + 4y = -2\]

We know y = -2 so sub that in...

\[\large 3x + 4(-2) = -2\]
\[\large3x - 8 = -2\]
Add 8 to both sides...
\[\large 2x = 6\]
Divide both sides by 2
\[\large x = 3\]

Now we solved and the answer is x = 3 and y = -2

Answer 2

No no no hang on a second

Answer 3

made a slight error in the LAST bit of that...

After add 8 to both sides..it should be

\[\large 3x = 6\]
Then divide both sides by 3 not 2
\[\large x =2 \]

So x = 2 and y = -2

Answer 4

ahhh thank you so much for working it out step by step it helped me understand a lot @johnweldon1993

Answer 5

No problem @jadeedwardson :) if you need anymore help feel free to message me :)