Solving System of Linear Equations by Substitution: y=3x-4 and y=-1/2x+3

Published on March 27, 2026

Algebra

Find the intersection point of the lines y=3x-4 and y=-1/2x+3 by setting the expressions for y equal to each other and solving for x and y.

Question

y=3x-4 and y=-1/2x+3

Answer

The user has provided two linear equations and is likely asking to find the point of intersection of the two lines represented by these equations.

The two equations are:

Since both equations are set equal to

, we can set the right-hand sides equal to each other to solve for

Step 1: Eliminate the fraction by multiplying the entire equation by 2.

Step 2: Gather the terms on one side and the constant terms on the other side.
Add

to both sides:

Add 8 to both sides:

Step 3: Solve for .
Divide both sides by 7:

Step 4: Substitute the value of back into either of the original equations to find .
Using Equation 1:

Step 5: Verify the solution using the second equation (optional but recommended).
Using Equation 2:

Since both equations yield

when

, the point of intersection is

The solution is

and

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