Solve the system of equations by substitution:?

Question

Solve the system of equations by substitution:

x + 2y = 9
3x - y = 13

Answer 1

In order to solve this system of equations by substitution:

x + 2y = 9
3x - y = 13

Use the first equation and solve for x in terms of y:

x + 2y = 9

To do this, subtract 2y from both sides of the equation:

x + 2y = 9
= x + 2y - 2y = 9 - 2y
= x = 9 - 2y

Now, use this value, 9 - 2y, that equals x and substitue it into the second equation:

3x - y = 13
= 3(9 - 2y) - y = 13

Next, use the distributive property, which states that for numbers a, b, and c:

a(b + c) = ab + ac
a(b - c) = ab - ac

So:

3(9 - 2y) - y = 13
= 27 - 6y - y = 13

Combine like terms:

27 - 6y - y = 13
= 27 - 7y = 13

Subtract 27 from both sides of the equation:

27 - 7y = 13
= 27 - 7y - 27 = 13 - 27
= -7y = -14

Lastly, divide by -7 in order to solve for y:

-7y = -14
= -7y/-7 = -14/-7
= y = 2

Substitue this value of y into one of the original equations to solve for x and obtain your answer:

x + 2y = 9
= x + 2(2) = 9
= x + 4 = 9
= x = 5

This is your answer: x = 5 and y = 2, or in coordinate form (5, 2).

Hope this helps!

Answer 2

No sweat, just solve equation 1...
x= 9-2y
and put in equation 2:
3(9-2y) -y =13
Clear the ( ), collect y and constant terms on opposite sides of the "="
Solve for y.
Insert in equation 2 (somewhat easier than 1) and find x.
Validate by doing same in equation 1.

Answer 3

First guy: x = 9 - 2y

SUBSTITUTE this into the second guy:

3(9 - 2y) - y = 13
27 - 6y - y = 13
-7y = -14
y = 2

which means x + 4 = 9 or x = 5

Answer 4

substitute 4x for y so: 4x = 3x - 3 then move the x's to the same side by subtracting 3 x from 4x so: x = -3

Answer 5

x=5
y=2

Answer 6

y=2
x=5

You can sub those right back into the equation to check