Calculate the solution to these simultaneous equations using the elimination method: (1)(1)3ℎ−2𝑔3h−2g==1313 (2)(2)3ℎ+𝑔3h+g==−2−2
Question
Calculate the solution to these simultaneous equations using the elimination method: (1)(1)3ℎ−2𝑔3h−2g==1313 (2)(2)3ℎ+𝑔3h+g==−2−2
Solution
Sure, let's solve these simultaneous equations step by step:
Given equations are:
- 3h - 2g = 13
- 3h + g = -2
Step 1: Align the equations so that like terms and constants are in columns:
3h - 2g = 13 3h + g = -2
Step 2: Add the two equations together:
(3h - 2g) + (3h + g) = 13 + (-2)
This simplifies to:
6h - g = 11
Step 3: Solve for g:
g = 6h - 11
Step 4: Substitute g = 6h - 11 into the second equation:
3h + (6h - 11) = -2
This simplifies to:
9h - 11 = -2
Step 5: Solve for h:
9h = 9 h = 1
Step 6: Substitute h = 1 into the equation g = 6h - 11:
g = 6(1) - 11 g = -5
So, the solution to the system of equations is h = 1 and g = -5.
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