3x+5y=10 7x-15y=26
There are two variables in the equation
Yes, there are two variables, because these are
the equations of lines. If they intersect, there is
an x,y pair that satisfies both equations.
Multiply the first equation by 3.
3 * (3x + 5y) = 3 * 10
9x + 15y = 30
Add the second equation to that.
9x + 15y = 30
+(7x - 15y = 26)
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16x = 56
x = 3.5
Substitute that value of x into the first equation.
3x + 5y = 10
3(3.5) + 5y = 10
10.5 + 5y = 10
5y = 10 - 10.5
5y = -0.5
y = -0.5/5
y = -0.1
Use the second equation to verify the values.
7x - 15y = 26
7(3.5) - 15(-0.1) = 26
24.5 + 1.5 = 26
26 = 26
So, x = 3.5 and y = -0.1