Calculate the solution to these simultaneous equations using the substitution method: (1)(1)𝑟r==𝑡+5t+5 (2)(2)𝑟+3𝑡r+3t==−7−7
Question
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)𝑟r==𝑡+5t+5 (2)(2)𝑟+3𝑡r+3t==−7−7
Solution
Sure, let's solve these simultaneous equations step by step using the substitution method.
The given equations are:
- r = t + 5
- r + 3t = -7
Step 1: From equation (1), we know that r = t + 5. We can substitute this into equation (2) to eliminate r.
Step 2: Substituting r in equation (2), we get (t + 5) + 3t = -7.
Step 3: Simplifying this, we get 4t + 5 = -7.
Step 4: Solving for t, we subtract 5 from both sides to get 4t = -12.
Step 5: Finally, divide both sides by 4 to solve for t. So, t = -3.
Step 6: Now that we have t, we can substitute t = -3 into equation (1) to find r. So, r = -3 + 5 = 2.
So, the solution to the simultaneous equations is r = 2 and t = -3.
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