After clearing decimals, look at the coefficients of $x$ and $y$ in the two equations. Which variable has coefficients that can be turned into the same number with smaller multipliers?

Once the coefficients of $y$ match in size but are opposite in sign, add or subtract the equations so that $y$ disappears. What equation in $x$ alone do you get?

You will get an equation of the form $ax = b$. How do you isolate $x$ from there?

In Desmos, type each equation exactly as given, one per line: 0.2x - 0.5y = 2 and 1.5x + 0.3y = 6.9. Desmos will graph both lines and show their intersection point.

Tap or click on the point where the two lines intersect. Desmos will display the coordinates of this point $(x, y)$.

From the intersection coordinates, note the $x$-coordinate. That value is the solution for $x$ in the system.

Start with the system:

Multiply both equations by 10 to remove the decimals:

• First equation: $10(0.2x - 0.5y) = 10(2)$ becomes $2x - 5y = 20$.
• Second equation: $10(1.5x + 0.3y) = 10(6.9)$ becomes $15x + 3y = 69$.

Now work with:

Choose a variable to eliminate; $y$ is convenient because the coefficients $-5$ and $3$ can both be turned into $15$.

• Multiply the first equation by $3$:

• Multiply the second equation by $5$:

Now you have:

Add the two new equations together to eliminate $y$:

• Left side: $(6x - 15y) + (75x + 15y) = 6x + 75x + (-15y + 15y) = 81x$.
• Right side: $60 + 345 = 405$.

So you get a single-variable equation:

Solve the equation $81x = 405$ by dividing both sides by $81$:

So, the value of $x$ in the solution to the system is $5$.