Set Equations Equal: To find the intersection point of the two lines, we set the two equations equal to each other since at the point of intersection, both equations will have the same y value. So, we have -3x + 4 = 3x - 2.Solve for x: Now, we will solve for x by moving all terms involving x to one side and the constant terms to the other side. -3x + 3x + 4 = 3x - 3x - 2Combine Like Terms: Simplify the equation by combining like terms. 0x + 4 = 0 - 2Identify Parallel Lines: This simplifies to 4 = -2, which is a contradiction. This means that the two lines are parallel and do not intersect.

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$y=-3x+4$ $\newline$ $y=3x-2$

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Math Problems

Algebra 1

Solve linear equations with variables on both sides

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y=-3x+4

\newline

y=3x-2

Set Equations Equal: To find the intersection point of the two lines, we set the two equations equal to each other since at the point of intersection, both equations will have the same $y$ value. $\newline$ So, we have $-3x + 4 = 3x - 2$ .
Solve for x: Now, we will solve for $x$ by moving all terms involving $x$ to one side and the constant terms to the other side. $\newline$ $-3x + 3x + 4 = 3x - 3x - 2$
Combine Like Terms: Simplify the equation by combining like terms. $0x + 4 = 0 - 2$
Identify Parallel Lines: This simplifies to $4 = -2$ , which is a contradiction. This means that the two lines are parallel and do not intersect.