solve each system by substitution. check your answers 4y +3 = 3y +x and 2x +4y =18
4y +3 = 3y +x is y = (x - 3)
then
2 x + 4 (x-3) = 18
6 x - 12 = 18
6 x = 30
x = 5 etc
Thanks!
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To solve each system by substitution, we start by solving one of the equations for one variable and substituting that expression into the other equation. Let's solve the first equation for x:
4y + 3 = 3y + x
Rearranging the equation to isolate x, we subtract 3y from both sides:
x = 4y + 3 - 3y
Simplifying this expression, we get:
x = y + 3
Now, we substitute this expression for x into the second equation:
2x + 4y = 18
Replacing x with y + 3, we have:
2(y + 3) + 4y = 18
Expanding the expression and combining like terms, we get:
2y + 6 + 4y = 18
Combining y terms, we have:
6y + 6 = 18
Subtracting 6 from both sides:
6y = 12
Dividing by 6:
y = 2
Now that we have the value of y, we can substitute it back into the first equation to find x:
x = y + 3
x = 2 + 3
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 2.
To check our answer, we substitute these values back into the original equations:
For the first equation:
4y + 3 = 3y + x
4(2) + 3 = 3(2) + 5
8 + 3 = 6 + 5
11 = 11
The equation holds true.
For the second equation:
2x + 4y = 18
2(5) + 4(2) = 18
10 + 8 = 18
18 = 18
The equation also holds true.
Therefore, our solution of x = 5 and y = 2 is correct.