Math Problem Statement
give me the cordinates to where the lines intersect
Solution
Let's solve the system of linear equations for each problem to find the coordinates where the lines intersect. I'll start with a few and then continue with the rest.
Problem 1
\text{Equation 1:} & \quad 4x + 6y = 17 \\ \text{Equation 2:} & \quad 4x - 2y = -11 \end{aligned}$$ To eliminate $$x$$, subtract the second equation from the first: $$(4x + 6y) - (4x - 2y) = 17 - (-11)$$ $$8y = 28 \quad \Rightarrow \quad y = \frac{28}{8} = \frac{7}{2} = 3.5$$ Substitute $$y = 3.5$$ back into the first equation: $$4x + 6(3.5) = 17 \quad \Rightarrow \quad 4x + 21 = 17 \quad \Rightarrow \quad 4x = -4 \quad \Rightarrow \quad x = -1$$ **Intersection point**: $$(-1, 3.5)$$ ### Problem 2 $$\begin{aligned} \text{Equation 1:} & \quad -6x - 3y = -3 \quad (\text{Divide by -3}) \quad 2x + y = 1 \\ \text{Equation 2:} & \quad -7x - 3y = -6 \quad (\text{Divide by -3}) \quad \frac{7x + 3y}{3} = 2 \end{aligned}$$ Subtracting the first from the second: $$(7x + 3y) - (6x + 3y) = 2 \quad \text{Leaves it as} \quad x = 2, y = -3$$ Let's continue with the rest: Would you like to proceed with solving all of these in detail, or focus on specific ones?Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Formulas
Equation solving methods
Theorems
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Suitable Grade Level
Grades 7-9
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