Which properties justify the steps taken to solve the system?
{4x+3y=25
{2x+−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 _____________
The properites: Addition property of equality, subtraction property of equality, substitution property of equality, multiplication property of equality, division property of equality, commutative property of addition, and simplify
Fill in the correct blanks
The properites: Addition property of equality, subtraction property of equality, substitution property of equality, multiplication property of equality, division property of equality, commutative property of addition, and simplify
4x+3y=25 Addition property of equality
−4x+10y=−38 Multiplication property of equality
13y=−13 Simplify
y=−1 Division property of equality
4x+3(−1)=25 Substitution property of equality
4x−3=25 Simplification
4x = 28 Addition property of equality
x = 7 Division property of equality
Here is how the properties justify each step taken to solve the system:
Step 1: Adding -4x to both sides of equation 2
4x + 3y = 25; −4x + 10y = −38
By using the addition property of equality, we can add -4x to both sides of the equation to eliminate the x term on the left side.
Step 2: Dividing both sides of equation 2 by 10
−4x + 10y = −38
By using the division property of equality, we can divide both sides of the equation by 10 to isolate the y term and simplify the equation.
Step 3: Simplifying equation 2
13y = −13
By simplifying the equation, we can see that the coefficient of y is 1 and the constant term is -13.
Step 4: Dividing both sides of equation 3 by 13
y = −1
By using the division property of equality, we can divide both sides of the equation by 13 to solve for the value of y.
Step 5: Substituting y = -1 into equation 1
4x + 3(-1) = 25
By using the substitution property of equality, we substitute the value of y (-1) into equation 1 to solve for x.
Step 6: Simplifying equation 4
4x - 3 = 25
By simplifying the equation, we combine like terms on the left side.
Step 7: Adding 3 to both sides of equation 5
4x = 28
By using the addition property of equality, we add 3 to both sides of the equation to isolate the variable x.
Step 8: Dividing both sides of equation 6 by 4
x = 7
By using the division property of equality, we divide both sides of the equation by 4 to solve for the value of x.
The properties used in each step are as follows:
Step 1: Addition property of equality
Step 2: Division property of equality
Step 3: Simplify (no specific property)
Step 4: Division property of equality
Step 5: Substitution property of equality
Step 6: Simplify (no specific property)
Step 7: Addition property of equality
Step 8: Division property of equality