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2 answers:
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Answer:
Given: , y =6
To prove: x =7
On substituting the value of y =6 in the equation 7y = 8x -14 to solve for x.
or
42 = 8x -14 ......[1]
Addition Property of equality states that you add the same number to both sides of an equation.
Add 14 to both sides in equation [1];
42+14 =8x -14+14
Simplify:
56 = 8x
or
8x =56 ......[2]
Division Property of equality states that you divide the same number to both sides of an equation.
Divide by 8 to both sides of an equation [2];
Simplify:
x =7 Hence proved!
A two Column proof:
Statement Reason
1. 7y = 8x -14 Given
y= 6
2. 7(6) = 8x -14 Substitution property
3. 42+14 = 8x Addition property of equality
4. 56 =8x Simplify
5. x =7 Division Property of equality
Answer:
(-2.2, -1.6), (3, 1)
Step-by-step explanation:
You don't have to go far to find the equations. They are right there in your problem statement. Perhaps you want to find the solutions to the equations.
Use the first equation to write an expression for x, then substitute that into the second equation:
x = 2y +1
y^2 -3(2y+1)(y) +8 = 0
-5y^2 -3y +8 = 0
-(5y +8)(y -1) = 0
y = -8/5 or y = 1
The corresponding values of x are ...
x = 2(-8/5)+1 = -11/5
x = 2(1) +1 = 3
The solutions are (x, y) = (-2.2, -1.6) and (3, 1).
