2y=-x+93×-6y=-15 whats the solution to the system
2 answers:
Answer:
Step-by-step explanation:
2y = -x +9
3x - 6y = -15
The solution is the value of x and y that will make the two equations true in the same time.
3x-6y = -15; divide both sides by 3
x-2y = -5; substitute 2y for -x+9 because the first equation tell us they are equal
x-(-x+9) = -5; open parenthesis
x+x-9 = -5 ; add 9 to both sides and combine like terms
2x = -5 +9; 2x = 4; divide both sides by 2
x= 2
Substitute x for 2
2y = -x+9 ; 2y = -2 +9 ; 2y = 7; y = 7/2 = 3.5
Solution is (2, 3.5)
Answer:
(2, 7/2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality <u>Algebra I</u>
Coordinates (x, y) Terms/Coefficients Solving systems of equations using substitution/elimination Step-by-step explanation:
<u>Step 1: Define Systems</u>
2y = -x + 9
3x - 6y = -15
<u>Step 2: Rewrite Systems</u>
2y = -x + 9
[Division Property of Equality] Divide 2 on both sides: y = -x/2 + 9/2
<u>Step 3: Redefine Systems</u>
y = -x/2 + 9/2
3x - 6y = -15
<u>Step 4: Solve for </u><em><u>x</u></em>
Substitute in <em>y</em>: 3x - 6(-x/2 + 9/2) = -15 Distribute -6: 3x + 3x - 27 = -15 Combine like terms: 6x - 27 = -15 [Addition Property of Equality] Add 27 on both sides: 6x = 12 [Division Property of Equality] Divide 6 on both sides: x = 2
<u>Step 5: Solve for </u><em><u>y</u></em>
Define original equation: 2y = -x + 9 Substitute in <em>x</em>: 2y = -2 + 9 Add: 2y = 7 [Division Property of Equality] Divide 2 on both sides: y = 7/2
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