Question

Which properties justify the steps taken to solve the system? {4x+3y=252x+−5y=19 Drag the answers into the boxes to match each step. 4x+3y=25; −4x+10y=−38 13y=−13 y=−1 4x+3(−1)=25 4x−3=25 4x = 28 x = 7 Addition property of equalitySubtraction property of equalitySubstitution property of equalityMultiplication property of equalityDivision property of equalityCommutative property of additionSimplify

Answer 1

the other guy was kinda right

Explanation:

Answer 2

Addition property of equality:

if a =b then; a + c= b + c

Subtraction property of equality:

if a =b then; a - c= b - c

Substitution property of equality:

If x =y then, x substituted in for y in any equation and y can be substituted for x in any equation.

Multiplication property of equality:

if a =b then;
`a * c = b * c`

Division property of equality:

if a =b then;
`(a)/(c) =(b)/(c)`

Commutative property of addition

a + b = b+ a

Given the system of equation:

`4x + 3y = 25` ......[1]

`2x-5y = 19` .....[2]

According to Multiplication property of equality;

Multiply equation [2] by -2 to both sides we get;

`-4x + 10y = -38` ......[3]

Using Commutative property of addition;

Add equation [1] and [3] we have;

`4x + 3y +(-4x+10y) = 25+(-38)`

`13y = -13`

By division property of equality:

Divide by 13 both sides we get;

`y = -1`

using Substitution property of equality:

Substitute the value of y in equation [1], we get;

`4x+3(-1) = 25`

`4x -3= 25`

By Addition property of equality:

Add 3 to both sides we get;

`4x = 28`

Simplify:

x = 7