How do you solve the following system?: 2x - 4y = 5 , x-4y=3

2 Answers
Gió
Nov 13, 2015

I found:
x=2
y=-1/4

Explanation:

I would isolate x from the second equation and substitute it into the first:
x=3+4y
and so:
2(color(red)(3+4y))-4y=5 solve for y:
6+8y-4y=5
4y=-1
y=-1/4
Substitute this back into: x=3+4y
x=3+4(color(red)(-1/4))=3-1=2

mason m
Nov 13, 2015

Use substitution for x then plug back in with y.

Explanation:

If x - 4y = 3, then add 4y to both sides to get x = 4y + 3.

Knowing this, you can plug in 4y + 3 in the other equation in place of x since they are equivalent.

This results in: 2(4y + 3) - 4y = 5
Distribute the 2 to get: 8y + 6 - 4y = 5
Combine like terms on the left: 4y + 6 = 5
Subtract 6 from both sides: 4y = -1
Divide both sides by 4: color(red)(y = -1/4)

With this knowledge, plug y into either equation to determine the value of x, as such: x - 4(-1/4) = 3
Multiply (remember that a negative time a negative is positive): x + 1 = 3
Add 1 to both sides: color(red)(x = 2)

Thus, our ordered pair is (2, -1/4).

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