Question
or
Solve using elimination.
–10x + 9y = 2
10x − 7y = –6
Answers
GPT-4o mini
To solve the system of equations using the elimination method, we have the following two equations:
1. \(-10x + 9y = 2\) (Equation 1)
2. \(10x - 7y = -6\) (Equation 2)
To eliminate one of the variables, we can add the two equations together. Notice that the coefficients of \(x\) in both equations are opposites (\(-10x\) and \(10x\)). Thus, adding the two equations will eliminate \(x\):
\[
(-10x + 9y) + (10x - 7y) = 2 + (-6)
\]
This simplifies to:
\[
(9y - 7y) = 2 - 6
\]
\[
2y = -4
\]
Now, divide both sides by 2 to solve for \(y\):
\[
y = -2
\]
Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use Equation 1:
\[
-10x + 9(-2) = 2
\]
This simplifies to:
\[
-10x - 18 = 2
\]
Now, add 18 to both sides:
\[
-10x = 20
\]
Now, divide by -10 to solve for \(x\):
\[
x = -2
\]
Thus, the solution to the system of equations is:
\[
(x, y) = (-2, -2)
\]
Final answer: \((-2, -2)\)
1. \(-10x + 9y = 2\) (Equation 1)
2. \(10x - 7y = -6\) (Equation 2)
To eliminate one of the variables, we can add the two equations together. Notice that the coefficients of \(x\) in both equations are opposites (\(-10x\) and \(10x\)). Thus, adding the two equations will eliminate \(x\):
\[
(-10x + 9y) + (10x - 7y) = 2 + (-6)
\]
This simplifies to:
\[
(9y - 7y) = 2 - 6
\]
\[
2y = -4
\]
Now, divide both sides by 2 to solve for \(y\):
\[
y = -2
\]
Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use Equation 1:
\[
-10x + 9(-2) = 2
\]
This simplifies to:
\[
-10x - 18 = 2
\]
Now, add 18 to both sides:
\[
-10x = 20
\]
Now, divide by -10 to solve for \(x\):
\[
x = -2
\]
Thus, the solution to the system of equations is:
\[
(x, y) = (-2, -2)
\]
Final answer: \((-2, -2)\)