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Math  /  Algebra

QuestionSolve using substitution. x=10−5x−7y=−15\begin{array}{l} x=10 \\ -5 x-7 y=-15 \end{array}

Studdy Solution

STEP 1

1. We have a system of equations, and we need to solve for both x x and y y .
2. The substitution method involves substituting the value of one variable from one equation into the other equation.

STEP 2

1. Identify the known value from the first equation.
2. Substitute the known value into the second equation.
3. Solve the resulting equation for the remaining variable.
4. Verify the solution by substituting both values back into the original equations.

STEP 3

Identify the known value from the first equation:
The first equation is x=10 x = 10 .

STEP 4

Substitute the known value of x x into the second equation:
The second equation is −5x−7y=−15 -5x - 7y = -15 .
Substitute x=10 x = 10 into this equation:
−5(10)−7y=−15 -5(10) - 7y = -15

STEP 5

Simplify the equation:
−50−7y=−15 -50 - 7y = -15

STEP 6

Solve for y y :
Add 50 to both sides:
−7y=−15+50 -7y = -15 + 50
−7y=35 -7y = 35
Divide both sides by −7-7:
y=35−7 y = \frac{35}{-7}
y=−5 y = -5

STEP 7

Verify the solution by substituting both x=10 x = 10 and y=−5 y = -5 back into the original equations:
First equation: x=10 x = 10 (True)
Second equation:
−5(10)−7(−5)=−15 -5(10) - 7(-5) = -15
Simplify:
−50+35=−15 -50 + 35 = -15
−15=−15 -15 = -15 (True)
Both equations are satisfied.
Therefore, the solution is:
x=10, y=−5 x = 10, \, y = -5

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