Question

1.
2x - y = 1
x + y = 2
solution:
coordinate grid image

Explanation:

Step1: Solve the system of equations

We have the system:

$$
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$$

Add the two equations together to eliminate \(y\):
\((2x - y)+(x + y)=1 + 2\)
\(2x - y+x + y=3\)
\(3x=3\)
Divide both sides by 3: \(x = 1\)

Step2: Substitute \(x = 1\) into one of the equations

Substitute \(x = 1\) into \(x + y=2\):
\(1 + y=2\)
Subtract 1 from both sides: \(y=2 - 1=1\)

Step3: Find the intersection point on the graph

The solution to the system of equations is the point where the two lines \(2x - y = 1\) and \(x + y = 2\) intersect. From the calculations, the intersection point is \((1,1)\). To graph the lines:

• For \(2x - y = 1\) (or \(y = 2x - 1\)): When \(x = 0\), \(y=-1\); when \(y = 0\), \(x=\frac{1}{2}\).
• For \(x + y = 2\) (or \(y=-x + 2\)): When \(x = 0\), \(y = 2\); when \(y = 0\), \(x = 2\).

Plot these points and draw the lines; they will intersect at \((1,1)\).

Answer:

The solution to the system of equations (and the intersection point of the two lines on the graph) is \((1,1)\)