Answer: See below.
Explanation:
First, we are already given these equations in standard form.
5x − 2y = 10
4x − 3y = 15
Next, we need to make the coefficients of the x variables opposites (as in 5 and -5, etc), since we want to eliminate the x's. To do this, we will find a common multiple (here, the Lowest Common Multiplb is 20). Then, we will multiply every term by the number that makes the coefficient of x our common multiple.
We will make the first equation with a coefficient of 20 for the x and the second with a coefficient of -20 for the x.
See this visually below.
5x − 2y = 10 ➜ 4(5x) − 4(2y) = 4(10) ➜ 20x - 8y = 40
4x − 3y = 15 ➜ -5(4x) − -5(3y) = -5(15) ➜ -20x + 15y = -75
Lastly, add these two equations together. The x's are eliminated. This also will let us solve for y.
20x - 8y = 40
+ -20x + 15y = -75
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7y = -35
y = -5