Pregunta
Solve. \[ \begin{array}{l}-4 x+10 y=-18 \\ -x+10 y=-12\end{array} \]
Ask by Lyons Edwards. in the United States
Feb 28,2025
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The solution is \( x = 2 \) and \( y = -1 \).
Solución
We start with the system of equations:
-4x + 10y = -18
-x + 10y = -12
Step 1: Subtract the second equation from the first.
(-4x + 10y) - (-x + 10y) = -18 - (-12)
Simplifying the left side gives:
-4x + 10y + x - 10y = -3x
The right side simplifies to:
-18 + 12 = -6
So, we have:
-3x = -6
Step 2: Solve for x.
Divide both sides by -3:
x = (-6) / (-3) = 2
Step 3: Substitute x = 2 into one of the original equations, for example, the second equation:
-x + 10y = -12
-2 + 10y = -12
Step 4: Solve for y.
Add 2 to both sides:
10y = -10
Divide by 10:
y = -1
Thus, the solution to the system is x = 2 and y = -1.
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Simplifique esta solución Beyond the Answer
To solve the system of equations: \[ -4x + 10y = -18 \quad \text{(1)} \] \[ -x + 10y = -12 \quad \text{(2)} \] We can use the elimination or substitution method. Here, let's eliminate \(y\). Step 1: Simplify equation (2) for \(x\): \[ -x + 10y = -12 \implies x = 10y + 12 \quad \text{(3)} \] Step 2: Substitute equation (3) into equation (1): \[ -4(10y + 12) + 10y = -18 \] \[ -40y - 48 + 10y = -18 \] \[ -30y -48 = -18 \] \[ -30y = -18 + 48 \] \[ -30y = 30 \] \[ y = -1 \] Step 3: Substitute \(y = -1\) back into equation (3) to find \(x\): \[ x = 10(-1) + 12 \] \[ x = -10 + 12 \] \[ x = 2 \] The solution to the system of equations is: \[ (x, y) = (2, -1) \]
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