use the substitution method to solve the linear system.
9x+6y=3
3x-7y=-26
please show me an example of how to do it.
what is the slope of the line perpendicular to y= 3x-7?
9x+6y=3
3x-7y=-26
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Solve one equation for one of the variables in terms of the other; for example, solve equation 1 for y.
6y = 3-9x and
y = (3-9x)/6 which I would then reduce to
y = (1-3x)/2
then substitute this y for y in equation 2.
3x -7*[(1-3x)/2] = -26
3x -(7+21x)/2 = -26
You see that y has been eliminated. Continue and solve for x, then substitute this value into the other equation and solve for y. Finally, substitute both x and y into one of the equations to make sure those values satisfy the equation. Check my work.
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thanks!:-)
To solve a linear system using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's start with the second equation: 3x - 7y = -26.
Solving this equation for x:
3x = 7y - 26
x = (7y - 26) / 3
Step 2: Substitute the expression from step 1 into the other equation.
Now, substitute the expression x = (7y - 26) / 3 into the first equation: 9x + 6y = 3.
9((7y - 26) / 3) + 6y = 3
Multiply both sides by 3 to remove the fraction:
9(7y - 26) + 18y = 9
63y - 234 + 18y = 9
Add the like terms:
81y - 234 = 9
81y = 9 + 234
81y = 243
Divide both sides by 81:
y = 243 / 81
y = 3
Step 3: Substitute the value of y into the expression obtained in step 1.
Now, substitute y = 3 back into x = (7y - 26) / 3:
x = (7(3) - 26) / 3
x = (21 - 26) / 3
x = -5 / 3
Therefore, the solution to the linear system is x = -5/3 and y = 3.