Problem 71
Question
Explain how to solve a system of equations using the addition method. Use \(3 x+5 y=-2\) and \(2 x+3 y=0\) to illustrate your explanation.
Step-by-Step Solution
Verified Answer
By using the elimination method, we have \(x = 6\) and \(y = -4\).
1Step 1: Multiply the equations to make the coefficients of y the same for elimination
The equation system given consists of \(3x + 5y = -2\) and \(2x + 3y = 0\). Multiply the first equation by 3 and the second by 5: \[3(3x + 5y) = 3(-2) \] \[5(2x + 3y) = 5(0) \]. It becomes \[9x + 15y = -6\] and \[10x + 15y = 0\]
2Step 2: Subtract one equation from the other
Once the coefficients of y are equal in both equations, they can be subtracted from each other: \[(10x + 15y) - (9x + 15y) = 0 - (-6)\] which gives \[x = 6\].
3Step 3: Substitute x into one of the original equations
Substitute \(x = 6\) into the second original equation: \[2(6) + 3y = 0\], which simplifies to \[3y = -12\] and finally, \[y = -4\].
Other exercises in this chapter
Problem 67
Will help you prepare for the material covered in the first section of the next chapter. $$\text { Subtract: }-9 y^{4}-\left(-2 y^{4}\right)$$
View solution Problem 68
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View solution Problem 71
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Write a system of equati
View solution Problem 72
When using the addition method, how can you tell if a system of linear equations has no solution?
View solution