Question

1. 3x + y = 4

x - 2y = 6

Explanation:

Step1: Solve the system of equations

We have the system:

$$
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From the first equation, express \(y\) in terms of \(x\): \(y = 4 - 3x\).

Step2: Substitute into the second equation

Substitute \(y = 4 - 3x\) into the second equation \(x - 2y = 6\):

$$ x - 2(4 - 3x) = 6 $$

Expand: \(x - 8 + 6x = 6\)
Combine like terms: \(7x - 8 = 6\)
Add 8 to both sides: \(7x = 14\)
Divide by 7: \(x = 2\)

Step3: Find \(y\)

Substitute \(x = 2\) into \(y = 4 - 3x\):
\(y = 4 - 3(2) = 4 - 6 = -2\)
So the solution is \(x = 2\), \(y = -2\), which is the point \((2, -2)\) on the graph.

Answer:

The solution to the system of equations is \(x = 2\), \(y = -2\) (the point of intersection is \((2, -2)\)).