Answer:
x = 1.25
y = 2.5
(1.25, 2.5)
Step-by-step explanation:
ELIMINATION
To use elimination, multiply or divide the entire equation until either the "x" or the "y" are the same in both equations.
3x + 3y = 11.25 ÷ 3 => x + y = 3.75
4x + 2y = 10 ÷ 2 => 2x + y = 5
"y" in both equations is equal to 1.
Subtract one equation from the other. This will get rid of the variable "y" because y - y = 0.
. 2x + y = 5 Subtract each term
- x + y = 3.75 Do 2x-x=x and y-y=0 and 5-3.75 = 1.25
. x = 1.25 Solved for "x"
Substitute x = 1.25 into any of the equations to find "y".
4x + 2y = 10
4(1.25) + 2y = 10 Multiply 4 and 1.25
5 + 2y = 10 Isolate "y" now
2y = 10 - 5 Subtract 5 from both sides
2y = 5 Divide both sides by 2
y = 5/2 Answer in fraction form
y = 2.5 Answer in decimal form
The point as an ordered pair is (1.25, 2.5). Or x = 1.25 and y = 2.5.
SUBSTITUTION
To use substitution, rearrange one of the equations so that it equals an isolated variable. I will rearrange 4x + 2y = 10 and isolate "y".
4x + 2y = 10
2y = 10 - 4x Subtract 4x from both sides
y = 5 - 2x Divide both sides by 2
Substitute y=5-2x into the other equation, replacing "y".
3x + 3y = 11.25
3x + 3(5-2x) = 11.25 Use the distributive property multiplying over brackets
3x + 15 - 6x = 11.25 Combine like terms (3x - 6x = -3x)
15 - 3x = 11.25 Isolate "x" variable now
-3x = 11.25 - 15 Subtract 15 from both sides
-3x = -3.75 Divide both sides by -3
x = 1.25 Answer
Substitute x = 1.25 in any of the equations.
y = 5 - 2x
y = 5 - 2(1.25) Multiply 2 and 1.25
y = 5 - 2.5 Subtract
y = 2.5 Answer
The point as an ordered pair is (1.25, 2.5). Or x = 1.25 and y = 2.5.
